
Alexander Isak and Andy Robertson put the home team in control before the break, and while Daniel Munoz pulled a goal back in extremely controversial fashion for the visitors, Florian Wirtz made the game safe during additional time.
The result means Arne Slot's side have now moved up to fourth place ahead of Aston Villa on goal difference and are only six points from securing a top-five berth.
The ECHO was in attendance at Anfield - on a day where fans protested against planned season ticket prices - and here we run the rule over the performances of the Liverpool players.
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Freddie Woodman 8
Clutched one low dribbler from Johnson early on before save from Mateta sparked second and good later stops from the same player, Lacroix and Sarr, the latter which ended in the controversy of Palace's goal.
Tougher ask defensively but stuck to it and signs of link-up with Salah, and good assist for second. Escaped blunder before interval, though. Subbed.
Ibrahima Konate 6
Settled after slightly wayward opening, although some of his passing caused nerves to jangle. Happy to just get the ball clear on occasion.
Virgil van Dijk 7
Refused to stand on ceremony with some of his defending and looked to cajole Liverpool out from the back. Had to dig deep as Palace pressed late on.
Andy Robertson 7
Kept on his toes by the Palace attack but able to get forward on occasion and popped up to take second superbly. Subbed.
Dominik Szoboszlai 7
Solid rather than spectacular in the midfield battle that Liverpool began to edge before the break before becoming influential at both ends. Booked.
Alexis Mac Allister 7
Took a while to get up to speed but began to find his passes and mishit shot invited the opener. Inconsistent at times but good lay-off for the third.
Mohamed Salah 7
Enjoyed his tussles with Mitchell and Canvot down the right and strong run prompted the opener. Will hope his injury isn't the last we've seen of him in a Liverpool shirt. Subbed.
Florian Wirtz 8
Good pressing on occasion and used the ball well when in possession and swift good pass was integral to second. Won key balls and smashed in the third for deserved strike.
Plenty of endeavour first half in both directions but nullified by the Palace defence. Began to find spaces second half but wasn't helped by some poor officiating.
Alexander Isak 6
Most notable contribution was a defensive header until reacting quickly to improvise finish for opener. Looked a bit more like himself after that. Subbed.
Jeremie Frimpong (for Salah 59) 6
Much of his work was defensive as Palace turned up the pressure in the final half-hour.
Ryan Gravenberch (for Isak 79) 6
Brought on to help protect the defence.
Joe Gomez (for Jones 87)
A couple of good interventions.
Milos Kerkez (for Robertson 87)
Almost caught napping at far post but made up for it by clearing resultant long throw.