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An afternoon of defensive mishaps meant this match looked like it would end in an entertaining draw, but Spurs struck a late sucker-punch to secure a first win in five matches.
Substitute Sigurdsson rifled home from 25 yards to send White Hart Lane -- and head coach Sherwood -- wild, as Tottenham pulled back a two-goal deficit to win 3-2.
Few could have predicted this result given the way Saints raced into a deserved lead, thanks in no small part to Kyle Naughton.
First the right-back misjudged a long ball forward that Jay Rodriguez raced onto and coolly slotted home, before then giving away possession as captain Adam Lallana netted an equally-impressive strike.
The goals will have impressed watching England manager Roy Hodgson, who had been joined in the directors' box by Sherwood until the second goal saw him race down to the touchline just in time to see Nathaniel Clyne misread a Naughton cross, allowing Christian Eriksen to slot home.
The deficit was cancelled out completely within a minute of the second half as Roberto Soldado saw off the attention of Dejan Lovren to cross for the Dane to slot home and, just when the match looked to be ending level, Sigurdsson hammered home a fine winner.
Sherwood made five changes from Thursday's 2-2 draw at Benfica and one of those almost made an immediate impact, with Younes Kaboul powering an early header at Artur Boruc.
They continued to fling in crosses but without success as Saints defended diligently and attacked with gusto.
Southampton's first chance ended with Lallana blazing over a Rickie Lambert rollback, before Rodriguez found the net only for the offside flag to cut the visiting fans' celebrations short.
Saints' pressing was making life tough for the hosts, although it was a long ball from the back that proved their undoing in the 19th minute.
Boruc's goal kick was misread by Naughton and chased down by Rodriguez, who showed wonderful composure to fire a right-footed strike past Hugo Lloris.
The finish epitomised the confidence coursing through Southampton, which was again evident when Lallana showed quick feet to strike at Lloris.
Luke Shaw saw his attempt at a first Southampton goal blocked as Mauricio Pochettino's men continued in the ascendancy and it was no surprise when they doubled their advantage.
Naughton was again the guilty party, miscontrolling the ball into the path of Lambert, whose lay-off to the overlapping Lallana was struck low past Lloris in the 28th minute.
Boos rang out around White Hart Lane and Sherwood raced down to the bench to bark instructions, before the curse of the right-back struck in their favour.
Shortly after Nabil Bentaleb fizzed wide from distance, Naughton swung in a hopeful cross that was misread by Saints full-back Clyne, allowing Eriksen to sweep home and reduce the deficit.
Spurs midfielder Mousa Dembele hooked a volley wide soon after as Spurs were pushed on by the loud home support, although Lallana should have added a third for Saints when striking a Jack Cork pass straight at Lloris.
It was a missed opportunity they were made to rue as Spurs started the second half in the same manner they went into the break.
A lovely Soldado touch put Eriksen through on goal just before half-time, hurdling over challenges from Lovren and Jose Fonte, only to poke straight at Boruc.
The Southampton goalkeeper also had to push over a free-kick from the Dane, who would again find the net in the opening minute of the second half as Soldado outmuscled Lovren, cut inside and sent a low cross for Eriksen to slot home at the far post.
Sherwood, now back in the stands, pumped his fist with joy as his side played with renewed confidence, leading Soldado to strike from distance.
Saints' backline were coming under a lot of pressure as Soldado proved an increasing nuisance, highlighted when he chested the ball to Eriksen, whose ball over the top found Nacer Chadli.
The Belgium international's low strike looked like it may have been sneaking in at the near post before Boruc's interjection, with Eriksen getting behind in the same area soon after and firing into the side-netting.
Chadli saw weak penalty appeals against Shaw waved away as Spurs upped the ante, with substitute Calum Chambers' last-ditch challenge just enough to stop Eriksen finding the target.
Tottenham continued to press but with less gusto, which is perhaps why Sherwood returned to the bench, as Saints came close to snatching a winner through substitute Gaston Ramirez and then Lambert.
But then, out of nothing, Spurs completed a magnificent comeback as Eriksen squared for Sigurdsson to hammer home a superb last-gasp winner.
Premier League: Wins for Chelsea, Man City, Liverpool, Everton, Man Utd, Newcastle, Hull and Norwich
Yaya Toure scored a hat-trick as Manchester City hammered Fulham
Kieran Gibbs (L) is sent off by referee Andre Marriner (C) during the Premier League match between Chelsea and Arsenal
Chelsea and Liverpool both scored six on a high-scoring Premier League afternoon as fellow title contenders Manchester City knocked in five against bottom club Fulham.
Wayne Rooney scored a memorable goal as Manchester United picked up three points against West Ham United at Upton Park in Saturday Night Football.
Norwich City picked up a priceless win in their battle to avoid relegation after beating fellow strugglers Sunderland, while West Bromwich Albion were undone by two first-half goals at Hull City.
Everton continued their quest for Europa League qualification by edging a five-goal affair at home to Swansea City, while Crystal Palace were beaten by a last-gasp winner at Newcastle United.
Chelsea blew away Premier League title rivalsArsenal inside 17 madcap minutes at Stamford Bridge as Arsene Wenger's 1,000th game in charge turned horribly sour and ended in a humiliating 6-0 defeat.
The leaders went in front on five minutes when Andre Schurrle fed Samuel Eto'o after Arsenal ceded possession in the centre and the Cameroon forward turned Alex Oxlade-Chamberlain before curling a left foot shot beyond Wojciech Szczesny's despairing dive.
Arsenal gave the ball away once again two minutes later and then allowed Schurrle to advance unchecked to the edge of the box before he drilled a low shot into a static Szczesny's bottom corner.
Watch the Soccer Saturday team's reaction to Kieran Gibbs' wrongful dismissal in Arsenal's 6-0 loss to Chelsea.
The main talking point arrived soon after as Chelsea were awarded a penalty when Oxlade-Chamberlain dived to push an Eden Hazard shot, which looked to be heading wide anyway, past the post.
Referee Andre Marriner brandished a red card at a bemused Kieran Gibbs, rather than Oxlade-Chamberlain, while Hazard kept his nerve to convert down the middle of the goal after waiting for Szczesny to commit himself.
There was still time for Oscar to make it 4-0 before the interval, the Brazilian clipping home Fernando Torres' low cross from close range.
Szczesny was culpable in the 66th minute as he allowed a routine Oscar effort from outside the box to skip up off the turf in front of him to make it 5-0 before January signing Mohamed Salah got in on the act in the 71st minute, getting in behind the Arsenal defence to convert Nemanja Matic's ball over the top with a cool finish.
Yaya Toure scored a hat-trick, including two penalties, as Manchester City eased to a 5-0 home win over Fulham, who had Fernando Amorebieta sent off.
Despite scoring five goals against Fulham, Sky Sports pundit Charlie Nicholas believes Manchester City were lethargic.
City were ahead in the 26th minute when Toure scored from the penalty spot after Amorebieta was penalised for kicking Alvaro Negredo as the striker brought a long ball under control.
Toure repeated the trick on 54 minutes with another confidently dispatched penalty after Amorebieta, who had been booked for his foul on Negredo, was sent off after bringing down David Silva.
Ivory Coast midfielder Toure completed his hat-trick in sumptuous fashion on 65 minutes when he almost nonchalantly curled a 30-yard shot inside the upright and beyond a flailing David Stockdale.
Fernandinho arrowed a fourth goal into the top corner on 84 minutes before Martin Demichelis added the fifth with two minutes remaining by scuffing home a shot at the back post.
Sky Sports pundit Matt Le Tissier explains how Liverpool showed plenty of character to come from behind to beat Cardiff.
Luis Suarez scored a hat-trick, and Martin Skrtel netted a brace, as Liverpool twice came from behind in the first half before running out 6-3 winners over lowly Cardiff in south Wales.
A sloppy pass from Joe Allen contributed to Cardiff's opening goal on nine minutes as Fraizer Campbell capitalised on the mistake to set up Jordon Mutch for a low finish.
Liverpool were level seven minutes later when Jordan Henderson's excellent pass played in Glen Johnson and his low cross was turned home by Suarez.
Cardiff were back in front on 25 minutes as Campbell was played in down the right channel and the striker cut inside before driving a low shot past Simon Mignolet.
A look back at the action from Saturday's 3 o'clock kick offs with Jeff and the gang in the Soccer Saturday studio.
Yet Liverpool were level again before half-time as Cardiff failed to properly clear a corner and Skrtel pounced on some slack marking to convert Philippe Coutinho's cross.
The same two players combined to give Liverpool the lead nine minutes into the second half as Coutinho curled in a corner and Skrtel glanced his header past David Marshall.
It was Suarez's turn to get his second of the game on the hour mark after Cardiff failed to properly cut out Johnson's low cross and Daniel Sturridge's back-heel set up his strike partner to score.
Cardiff were again undone by poor defending on 75 minutes, this time from Steven Caulker, as Suarez was afforded the chance to roll in a low cross for Sturridge to guide past Marshall.
Two goals from Wayne Rooney, including a wonder strike from just inside the West Ham half, secured Manchester United a 2-0 victory at Upton Park.
Liverpool were similarly leaky at the back as Mutch helped himself to his second of the game with two minutes to go when the midfielder was left unmarked to head past Mignolet following Kenwyne Jones' knock-down.
The slipshod nature of Cardiff's defending was summed up in added time as Suarez shrugged Juan Cala off the ball before biding his time and slipping a shot past Marshall.
Manchester United followed up a midweek victory over Olympiakos with a 2-0 success atWest Ham thanks to Rooney's first-half brace.
Rooney opened the scoring after just eight minutes when he let fly from just inside the West Ham half and his looping shot left home keeper Adrian in a daze in front of former United midfielder David Beckham.
Sky Sports pundit Phil Thompson explains how Norwich overcame Sunderland at Carrow Road.
United, who had Michael Carrick playing at centre-half, added a second on 33 minutes following a quick counter-attack which ended with Rooney turning the ball home after Mark Noble's clearance from Ashley Young's cross went straight to the England international.
Sunderland remain in the drop zone after going down to a 2-0 defeat by relegation rivals Norwichat Carrow Road.
Norwich were in front on 20 minutes when Wes Brown's poor clearance went straight to Johan Elmander and he teed up Robert Snodgrass for an emphatic finish.
The Canaries' second goal was an absolute belter on 32 minutes when a headed clearance dropped to Alex Tettey 30 yards from the goal and the midfielder let fly with a stunning first-time volley which flew beyond Vito Mannone.
Roberto Martinez believes Everton showed maturity in their play after they beat Swansea 3-2 at home.
The Black Cats' miserable afternoon was compounded in the final minute when Marcos Alonso was sent off after being shown a second yellow card for handball.
Roberto Martinez enjoyed victory over his former club as Everton closed out a 3-2 win overSwansea at Goodison Park.
Everton took a 20th minute lead when Chico Flores brought down Ross Barkley just inside the box and Leighton Baines placed his penalty beyond the reach of Michel Vorm.
Swansea levelled just past the half-hour mark when Wayne Routledge's pass picked out Angel Rangel on the right of the penalty area and his low ball into the six-yard box was tapped in by Wilfried Bony.
Hull manager Steve Bruce says his team just about did enough to win their Premeir League match against West Brom.
The hosts regained the lead on 53 minutes when Romelu Lukaku fed Kevin Mirallas on the right and the winger's low cross was finished off by his fellow Belgian from close range.
Mirallas was also the creator of Everton's third goal five minutes later when his corner from the left was allowed to drift to the far post where Barkley stooped to head home.
Ashley Williams headed a Pablo Hernandez corner in off the bar in added time, but Everton saw out the closing moments to move up to fifth in the table.
Liam Rosenior scored his first goal for Hull City and Shane Long was on target against his old club as Steve Bruce's side beat West Brom 2-0 at the KC Stadium.
Sky Sports pundit Paul Merson believes Crystal Palace haven't got enough up front as they were beaten in the dying minutes by Newcastle.
Hull were in front on 32 minutes when Craig Dawson was penalised for an apparent foul on Long and, after Ben Foster saved Nikica Jelavic's penalty, Rosenior reacted the quickest to head beyond the stricken West Brom keeper.
The hosts doubled their lead six minutes later when West Brom failed to clear a corner and, after the ball was played back into the box, Long steered his shot beyond Foster.
Papiss Cisse headed home a last-minute winner as Newcastle snatched a 1-0 success over Crystal Palace at St James' Park.
Palace, who drew 0-0 at Sunderland a week ago, were holding out for a point until Cisse diverted Hatem Ben Arfa's cross beyond Julian Speroni.
