Spurs beat Bolton Wanderers 1-0 at White Hart Lane while City came from behind at home to beat Villa 3-1.
Spurs now have 67 points with two games to play, with City, who host Tottenham on Wednesday, fifth on 66, also with two games remaining.
Villa, with one game left, are on 64 and cannot now finish fourth. Liverpool, seventh on 62 points have to win their last two games to have any hope. The first of them is at Anfield on Sunday against title-chasing Chelsea.
Chelsea top the standings on 80 points, one ahead of Manchester United, who visit Sunderland on Sunday.
Arsenal are on 72 points and look certain to finish third. They visit Blackburn Rovers on Monday.
DEBUTANT BLUNDER
Events seemed to be going Tottenham's way as John Carew put Villa ahead early thanks to a blunder by debutant Man City goalkeeper Marton Fulop and Tom Huddlestone sumptuously shot Spurs ahead from 25 metres after 40 minutes against Bolton.
Considering the size of the prize it was a low-key opening 40 minutes at the City of Manchester stadium but the game exploded into life in a frantic last five of the first half.
Carlos Tevez equalised with a 41st-minute penalty after Stephen Warnock tripped Adam Johnson, Carew hit the bar for Villa a minute later then City broke and Emmanuel Adebayor put them 2-1 up.
The second half reverted to type with neither side showing the commitment to attack that might have been expected given the situation.
With Fulop, signed on an emergency loan from Sunderland in midweek, looking a nervous wreck, City's fans were gnawing their nails in the final stages.
They were no doubt cursing the club official who failed to insert a release clause in the loan agreement with Birmingham City that meant no return for Joe Hart to cover their goalkeeping injury crisis.
They were able to breathe again a minute from time when Shaun Wright-Phillips broke from his won half and set up Craig Bellamy for an emphatic finish.
"We didn't deserve to be behind but we continued to play well, got those two goals at the end of the first half," City manager Roberto Mancini told Sky Sports News.
"It was important that we continued to play football."
"I think we must beat Tottenham, it will be a massive game."
A season that promised so much for Villa ended in disappointment all round with defeat in the League Cup final, the FA Cup semi-finals and now their failure to qualify for the Champions League.
Spurs can still dream though after piling on the pressure in the second half at White Hart Lane. Jermain Defoe, Roman Pavlyuchenko, Gareth Bale and Peter Crouch all went close but they also needed a goalline clearance by Younes Kaboul to prevent Matt Taylor equalising.
They ran out deserved winners though and are now tantilisingly close to a first appearance in the Champions League.
In the day's other games bottom club Portsmouth beat Wolverhampton Wandere
