Manchester City are all but assured of a place in next season’s Champions League as Manuel Pellegrini’s time at the club ended with a draw at Swansea.
They were denied a win as Andre Ayew’s deflected free-kick cancelled out Kelechi Iheanacho’s close-range opener.
City’s vastly superior goal difference means United would need a 19-0 win over the Cherries to take fourth place.
And Arsenal finished second in the Premier League for the first time since 2005 as they beat relegated Aston Villa thanks to an Olivier Giroud hat-trick.
Giroud headed Arsenal ahead early on but the hosts played nervously until he struck again, sweeping home from six yards after good work by Mesut Ozil.
The Frenchman was then put through by Hector Bellerin for his third.
Mark Bunn’s own goal, diverting in Mikel Arteta’s ricocheted shot, added further gloss to the scoreline.
The comprehensive win ensured Arsenal leapfrogged faltering Tottenham – title contenders only a few weeks ago – after their north London rivals fell apart against Newcastle.
Meanwhile, 10-man Newcastle bid farewell to the Premier League with an extraordinary win over Tottenham, who finished third.
The display by the Magpies was scarcely believable. Georginio Wijnaldum fired in the opener and Aleksandar Mitrovic powerfully headed home for 2-0.
Erik Lamela reduced the deficit before Mitrovic was shown a straight red for a nasty foul on Kyle Walker.
Wijnaldum scored his second from the spot, and Rolando Aarons and Daryl Janmaat wrapped up the scoring, reports the BBC.
EPL RESULTS
Arsenal 1 – 0 Aston Villa
Chelsea 1 – 1 Leicester City
Everton 3 – 0 Norwich City
Newcastle United 5 – 1 Tottenham
Southampton 4 – 1 Crystal Palace
Stoke City 2 – 1 West Ham United
Swansea City 1 – 1 Manchester City
Watford 2 – 2 Sunderland
West Brom 1 – 1 Liverpool
Man United ? – ? AFC Bournemouth (Postp)
