Elsewhere, there were wins for Arsenal, Man United and Aston Villa.
Everton have guaranteed their survival in the Premier League.
A second half goal by Abdoulaye Doucoure gave them a 1-0 victory over Bournemouth at Goodison Park.
And that was enough to relegate both Leicester City and Leeds United.
Leicester City defeated West Ham 2-1 at the King Power Stadium, but they go down to the Championship seven years after winning the Premier League.
Leeds United were beaten 4-1 by Tottenham and return to the second tier after three years in the top flight.
Elsewhere, Brentford beat champions Manchester City 1-0
It ended Arsenal 5 Wolves 0, Aston Villa 2 Brighton 1, Chelsea 1 Newcastle United 1, Crystal Palace 1 Nottingham Forest 1, Manchester United 2 Fulham 1.
And relegated Southampton 4 Liverpool 4.
Tuesday Morning Sports Update
Ireland And England Will Meet Next February To Kick Off 2027 Six Nations
Tolka Park Stages The Dublin Derby Between Shelbourne And Shamrock Rovers
Conor McGregor Not Included In White House Fight In June
Ireland's Men And Women Hockey Teams Book Their Spot At This Year's World Cup
Ireland To Train Collectively Today Ahead Of Next Saturday's Six Nations Clash
Monday Morning Sports Update
Kildare Hurlers Seal 2027 Division 1B Place
