In the end, it was the Reds and the Blues who finished the season in third and fourth positions.
Leicester, meanwhile, needed to beat Tottenham Hotspur in order to give themselves a fighting chance of a top four finish but it was not to be.
In spite of two converted penalties from Jamie Vardy, the Foxes lost 4-2 to Spurs meaning they will miss out on Champions League football.
Chelsea lost their final game away against Aston Villa however, due to Leicester's defeat they retained their fourth spot.
Liverpool needed a victory over Crystal Palace to avoid any late top four drama. Two goals from Sadio Mane earned Jurgen Klopp's side their fifth straight victory and a third-place finish.
West Ham secure Europa League while Arsenal finish eighth
A 3-0 triumph for West Ham against Southampton sealed their place in the Europa League.
Pablo Fornals struck twice in quick succession to put David Moyes' team in control and Declan Rice made it safe with a third four minutes from time, much to the delight of the 10,000 supporters in attendance at the London Stadium.
Arsenal were set for a place in the Europa Conference League before Tottenham's dramatic comeback at Leicester. Nicolas Pepe continued his strong end to the campaign with a double in a 2-0 win at home to Brighton.
Everton's faint hopes of Europe were over early at the Etihad where Sergio Aguero marked his final appearance for Manchester City with a classy brace.
Pep Guardiola watched his team deliver a five-star showing in a 5-0 victory with Kevin De Bruyne, Gabriel Jesus and Phil Foden putting the champions three up before record goalscorer Aguero took centre stage.
Man United spoil Santo's farewell
Wolves were unable to give Nuno Espirio Santo one final win after a youthful Manchester United XI secured a 2-1 win on the road.
With an eye on Wednesday's Europa League final, teenagers Amad Diallo and Anthony Elanga were handed starts and the latter opened the scoring in the 13th minute with a bullet header.
Nelson Semedo cancelled out that effort, but a Juan Mata spot-kick in first-half stoppage time gave United all three points.
Sheffield United bade farewell to the Premier League with a seventh win of the season after David McGoldrick scored the only goal against Burnley at Bramall Lane.
Fulham were unable to give their fans anything to cheer after a tough campaign in the top flight as Joe Willock continued his remarkable form.
The Arsenal loanee netted for his seventh game in a row and Fabian Schar added a second to give Newcastle a 2-0 win at Craven Cottage while Leeds finished with a 3-1 win at home to West Brom in Sam Allardyce's final game.
Rodrigo and Kalvin Phillips put Marcelo Bielsa's side two up at the break and Patrick Bamford added a third from the penalty spot 11 minutes from time for his 17th goal of the season before Hal Robson-Kanu grabbed a consolation at the death.