Chelsea did more than they needed to, beating Wolves 2-0, while Man United also secured three points, winning by the same scoreline.
While the first half of Leicester vs United was rather uneventful, Chelsea burst into life on the brink of half-time at Stamford Bridge.
Mason Mount opened the scoring with a stunning free-kick in the first minute of added time, before Olivier Giroud rounded the goalkeeper to make it 2-0 less than two minutes later.
At half-time, Chelsea had all but qualified for the Champions League - and it was over to Leicester or Man United to fight over the remaining spot.
The second 45 minutes at King Power were far more open and Jamie Vardy had the best early chance after the break.
He flicked a header onto the bar from a Youri Tielemans free-kick on the hour mark. But then disaster struck at the other end.
Anthony Martial was fouled inside the box by a combination of Wes Mogan and Jonny Evans and the referee pointed to the spot.
Bruno Fernandes stepped up and converted from 12-yards to put United in the driving seat.
With the goal advantage, United saw out the game comfortably and even added a second at the death through Jesse Lingard.
Evans was also sent off for Leicester late on too.
Wolves failed to seriously threaten in the second half against Chelsea, meaning there was no late drama in London.
The full-time whistle blew simultaneously at Stamford Bridge at the King Power Stadium, confirming the results.
Man United and Chelsea finish on 66 points but it's Ole Gunnar Solskjaer's side who sit third with a superior goal difference, but fourth-placed Chelsea won't be worrying about that.
Leicester end the season in fifth, with 62 points.
Meanwhile Arsenal get revenge on Troy Deeney as they relegate Watford with 3-2 win
