Hull City crashed out of the Premier League on Sunday as Crystal Palace secured their own survival with a 4-0 thrashing of their relegation rivals at Selhurst Park.
Marco Silva's side knew only a victory would give them a realistic chance of staying up, but goals from Wilfried Zaha, Christian Benteke, Luka Milivojevic and Patrick van Aanholt consigned them to the drop.
Third-bottom Hull, winners just once in their last six matches, return to the Championship just 12 months after their promotion via the play-offs.
They paid the price for a chaotic campaign marred by poor signings and boardroom turmoil, not to mention conceding 13 penalties -- the highest in a Premier League season.
The Tigers will join already relegated Sunderland and Middlesbrough in the second tier next season.
Palace had needed a point to stay up and their dominant display completed boss Sam Allardyce's latest survival mission after he rescued Sunderland last season.
Swansea City's win at Sunderland on Saturday had left Hull with no margin for error and Palace's desire to secure their safety meant the stakes couldn't have been higher.
In the circumstances, the first goal would be crucial and Hull were getting a sinking feeling once again after Zaha punished a terrible blunder to open the scoring in the third minute.
Later in the day, Philippe Coutinho fired Liverpool within touching distance of the Champions League as the Brazilian inspired a 4-0 demolition of West Ham on Sunday.
Jurgen Klopp's side took the lead when Coutinho's sublime pass was converted by Daniel Sturridge in the first half at the London Stadium.
Coutinho stole the spotlight again in the second half with a superb solo strike and a cool finish to put Liverpool three goals ahead before Divock Origi netted to cap the Reds' swaggering display.
Liverpool moved back one point above Manchester City into third place in the Premier League.
Although City and fifth placed Arsenal both have a game in hand, Klopp's men will be guaranteed a Champions League berth if they beat relegated Middlesbrough at Anfield next Sunday.
In the event Arsenal lose at home to relegated Sunderland on Tuesday, Liverpool will clinch a top four spot without playing.