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.
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."
"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."
