Swansea needed a 10-goal swing - beating Stoke and seeing Southampton hammered by Manchester City - to stay up.
Andy King gave Swansea an early lead, but Badou Ndiaye and Peter Crouch scored before halftime to give Stoke only its second victory since Paul Lambert took charge in January.
Gabriel Jesus' dramatic victor at Southampton took City's Centurions to the 100-point mark - check out the stunning list of records the Blues have set this season. Along the way, they amassed a record-equalling 11 successive away wins, a feat previously achieved by Chelsea in 2008.
Jose Mourinho v West Ham Utd [audio]
Luke Shaw had a strike turned onto the post in the first half in a game bereft of quality. As for United, they actually secured 2nd place with a point.
Harry Kane did his best to chase Salah all the way at the top of the Premier League goalscoring charts, netting twice in Spurs' incredible win over Leicester, a game they twice trailed in.
Swansea and Stoke, two sides who conceded 124 goals between them this season, could only wish for such solidity at the back.
The season also included an unprecedented 18-game unbeaten run in the Premier League for City.
Dejan Lovren added a second before Dominic Solanke and Andrew Robertson scored their first goals for Liverpool to complete a routine victory in its last match before playing the Champions League final against Real Madrid on May 26. The confirmed teams can be seen, in full, below.
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Both sets of fans applauded Wenger in the 22nd minute of the game and two planes flew overhead dragging messages of support for the Frenchman.
"To enjoy it we had to win it - winning football games is what makes me happy and the boys did it", Wenger said. I think it's a record that will stay for a long time.
Gabriel Jesus, on as a substitute, found space to lift the ball over goalkeeper Alex McCarthy in the fourth minute of additional time, prompting wild celebrations among City's players.
City will celebrate on the streets of Manchester on Monday with an open-top bus parade.
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The all-new Google News replaces Google Play Newsstand on mobile and desktop and the Google News & Weather app on mobile. This will include headlines from different sources, videos, local news reports , social commentary and many more.