Dejan Kulusevski scored twice as Tottenham Hotspur held off Chelsea in the race for fifth place after a 3-0 victory at relegated Sheffield United.
Kulusevski struck after 14 minutes at Bramall Lane and, after Pedro Porro had increased the lead, doubled his tally to condemn the hosts to a seventh successive defeat.
Chelsea snatched a top-six finish with a hard-fought 2-1 victory over Bournemouth.
Moises Caicedo’s spectacular strike from just inside the Cherries’ half set the ball rolling and Raheem Sterling made it 2-0 just after the restart, but Benoit Badiashile’s own goal ensured a tense conclusion at Stamford Bridge.
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Newcastle needed a late strike from Bruno Guimaraes to fend off a Brentford fightback as a 4-2 win at the Gtech Community Stadium secured seventh place.
The Magpies looked to be cruising after first-half goals from Harvey Barnes, Jacob Murphy and Alexander Isak had put them 3-0 ahead, but Vitaly Janelt and Yoane Wissa dragged the hosts back into it before Guimaraes settled it.
A 2-0 win at Brighton could not prevent Manchester United from recording their lowest finish of the Premier League era.
Goals from Diogo Dalot and substitute Rasmus Hojlund inside the final 17 minutes secured three points but that was only good enough for eighth place, and they will miss out on Europe altogether if they fail to beat Manchester City in next weekend’s FA Cup final – a result which would hand Newcastle a Europa Conference League berth.
At the other end of the table, Chris Wood eased Nottingham Forest to safety with two goals inside the opening 14 minutes as they won 2-1 at relegated Burnley, for whom Ireland midfielder Josh Cullen scored.
That proved fatal for Luton, who succumbed 4-2 at home to Fulham with Raul Jimenez’s double and further goals from Adama Traore and Harry Wilson eclipsing Carlton Morris’s penalty and an Alfie Doughty strike.
Jean-Philippe Mateta’s hat-trick took some of the gloss off Aston Villa’s magnificent season as next season’s Champions League participants were trounced 5-0 by Crystal Palace at Selhurst Park.
Mateta’s treble was accompanied by a double for Eberechi Eze which edged the Eagles to a top-10 finish.
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