Defender Laurent Koscielny put visitors Arsenal ahead in the 52nd minute to secure fourth place with 73 points, one point ahead of fifth-placed Spurs who mustered a late goal from Gareth Bale to beat Sunderland 1-0 at White Hart Lane.
Chelsea sealed third place on 75 points with a 2-1 win at home to Everton.
Sunday, May 19:
Liverpool v QPR - MATCH REPORT
West Ham v Reading - MATCH REPORT
Manchester City v Norwich - MATCH REPORT
Swansea v Fulham - MATCH REPORT
Newcastle v Arsenal - MATCH REPORT
Southampton v Stoke - MATCH REPORT
Chelsea v Everton - MATCH REPORT
Wigan v Aston Villa - MATCH REPORT
West Brom v Manchester United - MATCH REPORT
Tottenham v Sunderland - MATCH REPORT
Chelsea 2 (Mata 7, Torres 76) Everton 1 (Naismith 14)
Liverpool 1 (Coutinho 23) QPR 0
Manchester City 2 (Rodwell 29, 59) Norwich 3 (Pilkington 26, Holt 54, Howson 65)
Newcastle 0 Arsenal 1 (Koscielny 52)
Southampton 1 (Lambert 57) Stoke 1 (Crouch 47)
Swansea 0 Fulham 3 (Kacaniklik 22, Berbatov 77, Emanuelson 90)
Tottenham 1 (Bale 90) Sunderland 0
West Brom 5 (Morrison 40, Lukaku 50, 81, 86, Mulumbu 81) Manchester Utd 5 (Kagawa 6, Olsson, 9-og, Buttner 30, Van Persie 53, Hernandez 63)
West Ham 4 (Nolan 23, 79, 87, Vaz Te 34) Reading 2 (McCleary 53, Le Fondre 55)
Wigan 2 (Boyce 21, Baker, 45-og) Aston Villa 2 (Bent 5, Vlaar 61)