The Icelandic international earned Spurs a point to leave them one point behind fourth-placed Arsenal and three back from the Blues with two matches remaining
Chelsea took an early lead when Oscar turned in a corner from close range at the back post before Spurs drew level through a superb 25-yard strike from Emmanuel Adebayor.
The Blues again went ahead six minutes before the break as Ramires broke through and produced a toe-poked finish into the bottom corner.
Rafa Benitez’s side had chances to seal the victory after the re-start but Spurs substitute Sigurdsson scored the visitors’ second equalizer of the game 10 minutes from time with a curling low shot.
The result means third-placed Chelsea is not yet assured of a place in the top four while qualification for the Champions League is out of Tottenham’s hands as it sits one point behind Arsenal with two matches to play.
Both sides made three changes to the starting line-ups that won their weekend matches, with Fernando Torres selected as Chelsea’s lone striker and Frank Lampard dropping to the bench as he chases Bobby Tambling’s club scoring record.
Spurs manager Andre Villas-Boas was dealt a blow as Mousa Dembele missed out with a muscle injury as Scott Parker and Lewis Holtby came into the side.
Villas-Boas spoke before the match of his belief that an attacking style of football is crucial as he returned to Stamford Bridge for the first time since being sacked in March last year - and both sides went on the attack during an open first 45 minutes.
Chelsea had the first chance of the game when Juan Mata fired over the crossbar in the seventh minute, but it only had to wait three more minutes to break the deadlock.
Mata swung in a corner from the right that Gary Cahill flicked on as he nipped in front of Michael Dawson and Oscar was on hand to head the ball home from close range.
In the 26th minute, Tottenham cleared a Chelsea corner and Scott Parker played the ball to Adebayor deep in his own half. The Togolese striker, so off form all season, ran at the Chelsea defense before curling a wonderful strike into the top corner past Petr Cech.
Six minutes before halftime, Chelsea once again took the lead. Fernando Torres did well to escape from Spurs defenders on the right touchline and slipped in Ramires, who at full speed toe-poked an unstoppable finish into the far corner.
Chelsea started the second-half with more purpose than the visitors and should have extended the advantage. Eden Hazard fired over from a tight angle before Ramires slipped when he looked certain to score after being played in by Mata.
But Tottenham took control as the second half wore on and Adebayor was again at the heart of the move as he produced a sublime first-time flick for substitute Sigurdsson to curl low into the corner from 12 yards out.