Rafa Benitez's men looked on course for the victory that would effectively secure a top-four finish after goals from Oscar and Ramires either side of Emmanuel Adebayor's stunner for Spurs.
But Sigurdsson stepped off the bench to curl home 10 minutes from time to leave the visitors three points adrift of Chelsea and one behind Arsenal with just two games to go.
Chelsea took the lead with 10 minutes on the clock when Oscar nodded home from close range at the far post after Gary Cahill had met Juan Mata's corner from the right with Tottenham's defence failing to pick up their men.
Spurs skipper Michael Dawson had to be brave to put his head directly in the way of a stinging Eden Hazard shot in the 25th minute after the Belgium international had cut inside Kyle Walker.
The visitors levelled moments later with a stunning effort from Adebayor, with the big striker picking the ball up inside his own half and advancing unchecked deep into Chelsea territory before passing the ball into Petr Cech's top corner.
Former Gunners forward Adebayor had a chance to top that stunning strike when he was picked out by Jan Vertonghen's vision, but he could not control his volley from 12 yards out and fired over the bar.
Benitez's men put their noses back in front in the 39th minute when Fernando Torres threaded a pass from out on the right through the Spurs defence for Ramires to burst onto and toe-poke his finish across Hugo Lloris and into the bottom corner.
Chelsea made a strong start to the second period and should have extended their lead when Hazard was found in space in the Spurs box, only to fire over the bar after leaving Walker on his backside with a neat turn.
They looked certain to make it 3-1 in the 61st minute when a sumptuous Hazard flick sent Mata racing away before squaring the ball to Ramires, only for the Brazilian to lose his footing at the crucial moment and go crashing to the turf.
Spurs weathered the storm and hit back, with Vertonghen's attempted overhead kick at the far post from Tom Huddlestone's free-kick going over the bar with Lewis Holtby in a better position to convert behind him.
Andre Villas-Boas' men levelled 10 minutes from the end when Benoit Assou-Ekotto's pass to Adebayor was neatly back-heeled by the big striker into the path of Sigurdsson to fire beyond Cech for a point which keeps Spurs in the race for the top four, although they remain behind both of their London rivals.