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The win allowed Liverpool to overtake Aston Villa in the league table, strengthening their position in the race for a top-four finish and Champions League qualification.
Alexander Isak opened the scoring in the 35th minute, netting his first goal since December after returning from injury, following an assist from Alexis Mac Allister.
Andrew Robertson doubled Liverpool’s lead five minutes later (40) with a pass from Curtis Jones.
Crystal Palace pulled one back through Daniel Muñoz in the 71st minute following a defensive lapse, but Florian Wirtz sealed the victory with a powerful strike in stoppage time (90+6).
Liverpool’s stand-in goalkeeper, Freddie Woodman, played a key role, making several crucial saves in the first half as injuries to regular keepers Alisson Becker and Giorgi Mamardashvili mounted.