Alexis Mac Allister put Liverpool ahead in the 40th minute, fellow midfielder Florian Wirtz doubled their advantage nine minutes after the restart and striker Alexander Isak sealed the win with an 89th-minute strike.
Liverpool return to winning ways and send Palace bottom
Liverpool ended a two-match losing run in all competitions with a 3-1 win at Crystal Palace on Sunday, piling more pressure on home manager Pierre Sage whose side slumped to a fourth straight Premier League defeat and fell to the bottom of the table.
Palace pulled a goal back deep into stoppage time when Eddie Nketiah converted a contentious penalty awarded after Liverpool left back Milos Kerkez and Palace forward Dario Osorio jumped for a header.
"I am very upset because the ones in our box they are calling penalties and in the other box they are not. I know we are 3-0 and it's the 95th minute but I'm very upset ...," Liverpool head coach Andoni Iraola told Sky Sports.
"It's a clash of heads. You can say it's 3-0 but, for me, there is more because it is not the first time this season and you compare ... I'm really upset.
"The VAR took a lot of time. When you call a penalty and they are two minutes. Two repetitions, three repetitions, they are finding a way not to be called by the VAR. A clean sheet is not cheap in the Premier League and we wanted to win 3-0.
"It is not just because of this penalty, it's because of a lot of things."
Liverpool arrived at Selhurst Park in need of a response after a 1-0 home league defeat by champions Arsenal last weekend and a 3-2 Champions League loss at Fenerbahce on Wednesday.
The win lifted Liverpool to fourth in the standings with 18 points from 10 matches, while Palace fell to 20th on seven points, with pressure continuing to mount on Sage.
