Arsenal stayed ahead of Manchester United in the race to qualify directly for next season's Champions League when they drew 1-1 at Old Trafford on Sunday while Manchester City made sure of their place in the group stage with a 4-2 win at Swansea City.
United are now left hoping Arsenal slip up in their last two home games so they can catch them, finish third and avoid a playoff for a place in Europe's top club competition.
With the season ending next weekend and the title already Chelsea's, the three behind them are still jockeying for the final positions.
Chelsea have 84 points with two games to play, City have 76 with one to play, Arsenal have 71 with two matches remaining while United have 69 with one to go.
Chelsea and City have guaranteed their direct qualification to the Champions League group stage, while Arsenal just need a point from their last two games, at home to Sunderland and West Bromwich Albion to make sure they join them.
Arsenal manager Arsene Wenger told Sky Sports after the game: "It was very important today not to let Manchester United get in front of us, even if we have a game in hand."
United manager Louis Van Gaal seemed to accept that United would most probably finish fourth and told Sky: "Then we will have to play a round to qualify because we have not qualified for the Champions League yet.
"What Arsene Wenger has said is right, it’s always stressful because you can meet an opponent who are halfway through their season already and we are just starting our season, so it’s not so easy.
"But of course I am satisfied, we set our goal at the beginning of the season and we have reached our goal. The fans seem pleased with us, that's fantastic, but I want more."
United went ahead when Ander Herrera volleyed in a cross from Ashley Young that beat David Ospina.
Arsenal equalised in the 82nd minute when a shot from Theo Walcott took a deflection off Tyler Blackett and flew past Victor Valdes, who had only come on seven minutes earlier to make his United debut.
The former Barcelona keeper, who has been at United since January, replaced the injured David De Gea, who could have made his last appearance at Old Trafford as a United player following widespread conjecture he will join Real Madrid next season.
Earlier Yaya Toure scored twice to lift Manchester City to a 4-2 win at Swansea after the hosts fought back from 2-0 down to level the scores.
Ivorian midfielder Toure struck his 50th league goal for second-placed City to give them a first-half lead and James Milner added a second.
Gylfi Sigurdsson pegged one back for Swansea with an excellent curling effort on the stroke of halftime and Bafetimbi Gomes struck his fifth goal in as many games to level the scores early in the second half.
As the hosts pushed on to complete a remarkable turnaround, Toure squeezed the ball in at the near post to restore the visitors' lead before City keeper Joe Hart made a stunning save to keep out a header from Federico Fernandez.
City's former Swansea striker Wilfried Bony added the fourth in stoppage-time.