The Togo international tapped in Clint Dempsey's low cross seven minutes from time to ensure Spurs head into the final day with their Champions League hopes alive.
Adebayor tapped home Clint Dempsey’s low cross with seven minutes left to complete a stirring Spurs turnaround facilitated by Charlie Adam’s rash dismissal on 47 minutes.
Adam had earlier crossed for Steven N’Zonzi to put Stoke in front in the opening minutes, but Dempsey equalized when he capitalized on a misunderstanding between Asmir Begovic and Marc Wilson.
The result means that, whatever the result when Arsenal takes on Wigan on Tuesday, Spurs will head into the final day of the season with their Champions League hopes very much alive.
Stoke pressed Tottenham early and hard, pushing the visitors back and forcing an uncertain visiting backline into mistakes, and inside three minutes the hosts had their reward. Adam curled an inviting free-kick delivery into the box from the right and N’Zonzi was left all alone at the near post to head past a floundering Hugo Lloris.
The Potters looked vulnerable in defense, though, and on 20 minutes, moments after seeing an effort correctly ruled out for offside, Dempsey made them pay. Wilson cleared a ball heading for Begovic but could only deflect it into the path of the American, who, with the Bosnian stranded upfield, lofted the ball into the empty net from 25 yards.
Tottenham – and in particular Gareth Bale – grew in confidence as the half drew to a close, but Stoke weathered the storm and the two sides went in level at the break. The decisive moment came just two minutes after the interval, as Adam received a second booking for sliding in rashly on Jan Vertonghen.
Almost immediately Spurs’ control of the game became total, and two minutes later Dempsey directed Bale’s devilish cross just over the bar with Begovic beaten.
Begovic continued to be the only point of significant resistance to Villas-Boas’ men, making crucial interceptions and saves as the visitors monopolized the ball and probed for an opening.
Even the Stoke No. 1 was helpless when Tom Huddlestone’s lofted in-swinging free-kick found Jan Vertonghen unmarked at the back post, but the defender headed just over.
The introduction of Mousa Dembele on 68 minutes gave Spurs greater guile, and soon after the Belgian threaded the ball into Bale, who, having checked onto his right foot, fired inches wide.
Stoke’s only threat came exclusively from set pieces, and 10 minutes from time Robert Huth headed narrowly over from a Dean Whitehead free-kick. Three minutes later, Adebayor prodded home the winner, one certain to make Arsenal fans everywhere feel more than a little uncomfortable heading into Tuesday's match against FA Cup winner Wigan.