Emmanuel Adebayor scored a late winner for Tottenham to keep their Champions League qualification hopes alive.
Stoke took the lead when Steven Nzonzi headed in Charlie Adam's free-kick.
Clint Dempsey fired into an empty goal after a mix-up in Stoke's defence to level before Adam was sent off after the break for a second yellow card.
Adebayor got the crucial second that put Tottenham up to fourth as he tapped home from close range following Dempsey's low cross into the area.
Villas-Boas praises 'patient' Spurs
Arsenal still remain in control of their own fate as they have two games remaining - against Wigan and Newcastle - while Tottenham have just one more game, at home to Sunderland, and are relying on their north London rivals slipping up.
But after a draw in midweek against Chelsea, Tottenham knew three points was a must at the Britannia Stadium to stay in the race.
Their opponents, safe from the drop after halting a dismal winless run to take seven points from their last three games, were obviously keen to put in a performance on their 150th anniversary.
The home fans were all kitted out in red-and-white T-shirts laid on by the club to mark the occasion and it was not long until they had something else to celebrate.
The score remains the same
All five Premier League matches between Stoke and Tottenham at the Britannia Stadium have now finished with a 2-1 scoreline, Spurs on top three games to two
Adam swung in a free-kick in the third minute and Spurs were caught flat-footed - particularly Adebayor - as Nzonzi coasted towards the near post to head home, via keeper Hugo Lloris's glove and the post.
Dempsey thought he had pulled the visitors level with a clever flick but it was ruled out for offside.
However, the American was soon handed another opportunity to bring the sides level when his ball for Aaron Lennon was cut out by Marc Wilson and came back to his feet.
With Begovic out of his goal having come for the initial ball, Dempsey turned the ball into the empty net from distance.
Tottenham probed for a second but for all their possession around the Potters' area, they could not create a clear opening until five minutes before break.
Referee made poor decision - Pulis
Gareth Bale put in a free-kick that Michael Dawson rose to head but Begovic pushed it away.
The Welsh winger then had a chance of his own when Scott Parker put him through - but again the hosts' keeper denied Spurs.
However, when Adam was given a second yellow card by referee Kevin Friend for a trip on Jan Vertonghen just 78 seconds into the second half, the London side's prospects brightened.
Boss Andre Villas-Boas was urging his players on as Vertonghen wasted an excellent chance when he headed Tom Huddlestone's free-kick over from six yards out.
Bale, Tottenham's hero so often this season, then created space in the area with a clever turn before sending his shot was just wide.
But it was Adebayor who proved the saviour this time as he turned home with seven minutes to go, Wilson heading over a late chance for Stoke.
Stoke manager Tony Pulis:
"I don't think Charlie has touched (Jan) Vertonghen on the first one and on the second one he's made a mistake by sliding in, but again I don't think he touches him.
"We're disappointed in particular with their second goal because it was a deflection that let their lad in.
"I'm delighted for us to be in the Premier League for a sixth consecutive season.
"It's not just what the club have done on the pitch, it's what the club has achieved behind the scenes as well."
Tottenham manager Andre Villas-Boas:
"What we did was we kept the patience. It would have been very easy for us to lump it forward. We were rewarded in the end for that patience. In the end we got what we deserved.
"It is not easy - we had to be very patient but in any set play Stoke would have a chance to score again.
"It was difficult to break them down."
On needing Arsenal to slip up:
"Hopefully we can be rewarded for what we have done this season. This result enables us to play at home to Sunderland, and Arsenal have a tough trip to Newcastle.
"This puts more pressure on Arsenal but they are able to cope with it. We hope Wigan have their day."
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