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Liverpool and Chelsea secured the final two Champions League qualification spots on a thrilling last day of the Premier League season, with Leicester missing out in the three-way fight for a top-four finish on Sunday.

Chelsea’s 2-1 defeat at Aston Villa didn’t prove critical because Leicester conceded three late goals to lose 4-2 at home to Tottenham and stay in fifth place.

Liverpool beat Crystal Palace 2-0 thanks to two goals from Sadio Mane and jumped into third place, two points above fourth-place Chelsea.

Leicester, which also missed out on Champions League qualification by losing on the final day of last season, was leading 2-1 after 76 minutes, only for goalkeeper Kasper Schmeichel to punch the ball into his own net. Substitute Gareth Bale scored in the 87th and again in stoppage time as Leicester poured forward in search of a winner.

West Ham beat Southampton 3-0 to finish in sixth place to qualify for the Europa League and Tottenham’s win at Leicester ensured the team got into the new Europa Conference League.

Sergio Aguero marked his final Premier League game for Manchester City by scoring twice as a substitute in the champions’ 5-0 win against Everton.

Harry Kane finished as the league’s top scorer, for the third time, on 23 goals — one ahead of Liverpool’s Mohamed Salah — after scoring at Leicester. The striker also had more assists than anyone else, with 14.

Arsenal failed to qualify for European competition for the first time in 25 years after finishing in eighth place, a point behind north London rival Tottenham, despite beating Brighton 2-0.

There were also wins for Manchester United, Newcastle, Leeds and Sheffield United.