Tottenham Hotspur snatched a late 1-1 home draw with Blackpool on Saturday but it was probably not enough for their hopes of securing fourth-place in the Premier League even though Manchester City were beaten by Everton.
With three games remaining, City, who face Stoke City in the FA Cup final next week, are fourth on 62 points with Spurs fifth on 56 and Liverpool on 55.
Arsenal, who visit Stoke on Sunday, have 67 points while Chelsea are second on 70 and Manchester United top on 73 ahead of their crunch title clash at Old Trafford on Sunday.
West Ham United ended a run of five defeats with a 1-1 home draw against Blackburn Rovers but remain bottom of the standings and favourites for relegation.
Everton's win was their seventh in eight meetings with City but it looked unlikely as the visitors dominated the first half.
David Silva looked a class above anyone else on the pitch but though he set up Yaya Toure for the 28th-minute opener City wasted several other good chances and paid a heavy price.
Sylvain Distin equalised against his former club in the 65th minute and seven minutes later Phil Neville swung in a cross which Leon Osman thumped in with a magnificent header.
"It was impossible to lose this game today after all the chances we had," City manager Roberto Mancini told Sky Sports.
"The players need to learn that when we have a chance to score we can't be selfish, it's not important who scores."
The Italian, however, had no concerns about hanging on to fourth place. "We don't have a problem for this...if we had won today we could have prepared very well for the FA Cup final but now we'll have to play very hard on Tuesday."
Everton remain seventh and manager David Moyes said: "A brilliant performance by our players in the second half, though it didn't look likely after 45 minutes.
"Then we started showing our spirit and our attitude and it was a great goal to win it."
That result gave hope to Spurs but it was Blackpool, who beat them in February for their solitary win in the last 16 games, who created most of the chances.
Heurelho Gomes, who had blundered on several occasions in recent weeks, had kept Spurs in the game with several good saves, the best of them a brilliant penalty stop from Charlie Adam after 75 minutes.
Seconds later though he charged from his goal and brought down Gary Taylor-Fletcher to give away a second penalty and this time Adam went the other way to score.
Defoe's shot out of the blue set up a desperate finale but with away games at City and Liverpool up next, Tottenham's dream of another crack at the Champions League looks over.
There was also concern for PFA Player of the Year Gareth Bale who was carried off on a stretcher with an ankle injury after being caught by a wild-looking tackle from Adam that could have resulted in a red card.