Jay Rodriguez opened the scoring with a neat strike in the 19th minute after a Kyle Naughton blunder allowed him to latch on to a long kick from goalkeeper Artur Boruc.
Premier League
1 Chelsea 69
2 Liverpool 65
3 Man City 63
4 Arsenal 62
5 Tottenham 56
6 Everton 54
7 Man Utd 51
8 Newcastle 46
9 Southampton 45
10 Stoke City 37
11 A Villa 34
12 Hull City 33
13 Norwich 32
14 West Ham 31
15 Swansea 29
16 West Brom 28
17 C Palace 28
18 Sunderland 25
19 Cardiff 25
20 Fulham 24
Another Naughton mistake was punished nine minutes later as he lost the ball on the edge of the area and Adam Lallana coolly slotted the ball home after being played in by a clever Rickie Lambert pass.
However, Spurs were gifted a lifeline just after the half-hour mark when Nathaniel Clyne failed to clear a right-wing cross and Christian Eriksen was able to fire in at the back post.
Eriksen equalised in the opening minute of the second half with another close-range finish after Roberto Soldado had shrugged off the challenge of Dejan Lovren before delivering an excellent low cross.
It looked like both sides would have to settle for a point as the clock ticked down in an exciting finale, but Sigurdsson drilled a powerful shot into the bottom corner from distance in injury-time to boost Spurs' hopes of European qualification and leave Saints stunned.
Stoke came from behind to seal a stunning 4-1 victory over Aston Villa at Villa Park - the first time they have ever scored four goals in a Premier League away game.
Paul Lambert's Villa hosts were looking to make it three home wins on the spin after back-to-back victories over Norwich and Chelsea - and they made the perfect start when Christian Benteke blasted home a left-footed strike on five minutes following a fine pull-back from Fabian Delph.
The Potters were on level terms on 22 minutes, though, as Peter Odemwingie latched onto a flick-on from Peter Crouch then outmuscled Ryan Bertrand before dinking the ball under the body of Villa goalkeeper Brad Guzan.
The visitors went ahead four minutes later when Erik Pieters' left-wing cross found Crouch, who coolly sidefooted the ball past Guzan to make it 2-1.
And Mark Hughes' men scored the goal of the game on 42 minutes, when a fine flowing passage of patient passing was rewarded when Steven Nzonzi pounced on a defensive slip from Nathan Baker to steer a low, right-footed shot into the back of the net from 18 yards out.
The four first-half goals took this weekend's tally to a whopping 41, with the most goals scored on a Premier League weekend being 43 in February 2011.
And it was Stoke who put the icing on the cake with a late fourth goal. Marko Arnautovic breezed past Leandro Bacuna on the left flank and pulled the ball back to Geoff Cameron, who sidefooted home on 90 minutes.
The win saw the Potters leapfrog Villa in the table to go 10th on 37 points.