Gareth Bale fired a lacklustre Tottenham Hotspur to a last-gasp win against former club Southampton on Saturday to keep their Champions League hopes alive.
However, they were unable to gain over fellow London challengers Arsenal who jumped up to third with a 1-0 win over relegated QPR.
At the bottom end, Wigan Athletic boosted their hopes of survival with a resilient 3-2 win at West Bromwich Albion.
Bale was this week named the Football Writers' Association Player of the Year, to go with his double success at the Professional Footballers' Association Player of the Year awards, and he proved his worth once again with his 25th goal of the campaign.
Kick-off at White Hart Lane had been delayed by half an hour due to a nearby motorway closure and Southampton looked set for a hard-earned point until Bale struck with four minutes to play.
Collecting possession wide on the right, the Welshman cut inside and shrugged off Luke Shaw before arrowing a crisp drive into the bottom-left corner from 25 yards.
At Loftus Road, Theo Walcott scored the quickest Premier League goal of the season after 20 seconds to give Arsenal victory and keep them a step ahead of rivals Spurs and Chelsea in the race for the Champions League.
Arsenal are above Chelsea in fourth but the Blues have two games in hand, their first at Manchester United on Sunday.
Callum McManaman scored a late winner as Wigan gave themselves renewed hope of avoiding relegation by twice coming from behind to win at West Brom.
The home side twice took the lead at the Hawthorns, through Shane Long and Gareth McAuley, only for Wigan to reply on each occasion through Arouna Kone and substitute James McArthur, who scored with his first touch.
McManaman netted the decisive goal in the 80th minute, side-footing home from close range after a superb run down the left from Shaun Maloney.
The FA Cup finalists are now just two points below fourth-bottom Sunderland, who host Stoke City on Monday, and three points adrift of Newcastle United, who could only draw 0-0 at West Ham United.
Gabriel Agbonlahor may have secured Aston Villa's top-flight status for another year after scoring an 89th-minute winner in a 2-1 success at Norwich City.
Villa, who thrashed Sunderland 6-1 on Monday, took a 55th-minute lead when Agbonlahor drove forward from the halfway line before planting a shot into the bottom-left corner from the edge of the 18-yard box.
Grant Holt equalised from the penalty spot with 16 minutes to play, but Agbonlahor struck again at the death to send Paul Lambert's team five points clear of danger, albeit having played a game more than third-bottom Wigan.
Elsewhere, deposed champions Manchester City were held to a 0-0 draw at Swansea City in a forgettable game at the Liberty Stadium.
The visitors' best chance fell to Edin Dzeko, who somehow contrived to shoot wide from Pablo Zabaleta's pass in the ying stages.
The result left Roberto Mancini's men 13 points behind champions Manchester United, who could now move 16 points clear at the summit with victory at home to third-place Chelsea on Sunday.
Hal Robson-Kanu scored twice as relegated Reading secured only their second away win of the season with a 4-2 success at Fulham, who fell to 13th place.
The Welsh international opened the scoring with a 12th-minute penalty and curled in his second goal 17 minutes into the second half.
Bryan Ruiz hit back twice for Fulham, either side of a 75th-minute strike by Adam Le Fondre, but Jem Karacan made sure of victory with a low shot in the 83rd minute.
Hull City secured a place in the Premier League for next season earlier on Saturday after drawing 2-2 at home to already-promoted Cardiff City on the final day of the Championship season.
Watford, Brighton and Hove Albion, Crystal Palace and Leicester City will contest the play-offs.