The Iceland international shot low past Petr Cech on 80 minutes to deny Chelsea, who were twice ahead, a victory that would have effectively guaranteed the hosts a top four finish and Champions League football next season.
With two matches remaining, third-placed Chelsea remain in pole position on 69 points, followed by Arsenal (67) and Spurs (66).
Chelsea went ahead on 10 minutes through Oscar's close-range header but a stunning Emmanuel Adebayor strike from 25 metres hauled Spurs level 16 minutes later.
Ramires rifled Chelsea back in front six minutes before half-time but Spurs finished strongly and Sigurdsson struck from Adebayor's cushioned back-heeled layoff.
Spurs have still not won at Stamford Bridge since 1990.
Andre Villas-Boas, booed by Chelsea fans on his return to West London after he was sacked by Roman Abramovich in March last year after less than nine months in charge, acknowledged Spurs face an uphill task to get back among the continent's elite.
"The result did not quite turn out how we wanted it and our situation changes slightly because now our fate is not in our own hands and we have to rely on others to slip up," the Portuguese told reporters.
"Anything can happen. The Premier League is completely unpredictable. These next fixtures before the emotional last day of the season can be decisive."
Chelsea visit Aston Villa on Saturday before hosting Everton on the final day on May 19, Arsenal are at home to Wigan on Tuesday and finish at Newcastle while Spurs play away at Stoke on Sunday and then welcome Sunderland to White Hart Lane.
"We have to win one game to guarantee top four, we will try to win both to be in the top three," said Chelsea interim manager Rafael Benitez.
"We had chances to score the third goal on the counter-attack we had chances to kill it. It was an open game, it was good for the fans, but not for us.
"Their second goal was offside but still, we had to defend it better. We controlled the game but we ran out of legs, we were tired, especially in the wide areas."
The last two matches between Chelsea and Spurs had produced 12 goals and an entertaining clash did not disappoint.
Chelsea struck first when Gary Cahill headed goalwards from a corner and Oscar nodded home.
Spurs had been on the back foot for much of the first half until Adebayor, picking the ball up inside his own half, was allowed to run towards goal before unleashing a swerving shot that nestled in the top corner.
Neat interplay involving Oscar and Fernando Torres on the right flank created the opportunity for Chelsea to restore their lead with Ramires latching on to a pass from Torres to toe-poke a first time shot past Hugo Lloris.
Ramires wasted a great opening after the break when he slipped in the penalty area and the tiring hosts were made to pay when a fine piece of skill from Adebayor allowed Sigurdsson the chance to salvage a point.
