Tottenham Hotspur secured Champions League football for next season by beating Newcastle, while Chelsea's top-four hopes got slimmer following a draw at Huddersfield, whose safety from relegation was confirmed.
Chelsea needed a fortunate goal from Marcos Alonso to salvage a 1-1 home draw with Huddersfield, who pulled four points clear of the relegation zone and all but doomed Swansea City.
The Terriers took the lead five minutes after half-time when City goalkeeper Willy Caballero misplayed a long ball forward and Laurent Depoitre capitalised on his mistake for the breakthrough.
Chelsea responded 12 minutes later when Mathias Jorgensen tried to clear the ball from the six-yard box but only smashed it against the face of Alonso -- and it crossed the line for the equaliser.
Huddersfield keeper Jonas Lossl did well to preserve the draw under Chelsea pressure, but the Blues could not find a winner and must now win at Newcastle on Sunday and hope Liverpool lose at home to Brighton to qualify for the Champions League.
The result also means Swansea will be relegated on Sunday unless they can beat Stoke while Southampton lose to Manchester City and overturn a goal difference of nine in the Saints' favour.
Harry Kane scored his 28th league goal of the season to help Tottenham beat Newcastle 1-0 to move past Liverpool into third place and a guaranteed top-four finish.
Kane turned a pass from Son Heung-Min into the top corner with his first touch to put Spurs ahead in the 50th minute, and Mauricio Pochettino's side held on to pull four points clear of Chelsea, ensuring a second straight season of Champions League football.
With his goal, Kane kept up a chance of catching Mohamed Salah for the Golden Boot, as he now will need a hat trick against Leicester to match the Liverpool attacker.
Leroy Sane provided three assists as Champions Manchester City set an assortment of Premier League season records after beating Brighton and Hove Albion 3-1 in Yaya Toure's farewell to the Etihad Stadium.
Danilo, Bernardo Silva and Fernandinho were on the scoresheet for City, who overcame Brighton's early equaliser through Leonardo Ulloa.
With the win, City reached 97 points on the season, breaking Chelsea's record from 2004-05 for the most in a Premier League season.
City's 31st win also broke a tie with Chelsea's team last season for the most in a single campaign, while Silva's goal was City's 104th of the season -- breaking Chelsea's record of 103 set in 2009-10.
Toure captained the side in his first Premier League start of the season and played 85 minutes.
A rotated Arsenal side lost 3-1 to Leicester City, the Gunners' seventh straight road defeat in the Premier League.
Leicester took the lead in the 14th minute when -- after a goalmouth scramble -- a cross to the back post found Fousseni Diabate, whose headed pass back across the box was lashed home by Kelechi Iheanacho.
Minutes later the hosts would go up a man for the rest of the match when Arsenal defender Konstantinos Mavropanos hauled down Iheanacho, who would have had a clear path to goal, after a bad giveaway and was shown straight red for the foul.
Arsenal drew level in the 53rd minute when Pierre-Emerick Aubameyang put back his own rebound from an Ainsley Maitland-Niles' cutback pass after Eldin Jakupovic had saved his first attempt.
Jamie Vardy put Leicester back into the lead on 76 minutes, coolly dispatching a spot kick after Henrikh Mkhitaryan had fouled Demarai Gray in the penalty area. Riyad Mahrez added Leicester's third in the 90th minute on the counter-attack, expertly beating his defender and firing into an open net to reach the final scoreline.
The result ended Arsenal's 22-match unbeaten league run against Leicester, their longest run against an opponent in their top-flight history.