Liverpool reduced Manchester City's advantage at the top to nine points after a 3-1 victory over Palace, who have lost each of their last 10 league meetings with the Reds.
Virgil van Dijk placed Jurgen Klopp's side in control after just eight minutes at Selhurst Park with his 10th headed goal in the competition – only Sami Hyypia (17) has scored more headers for the Reds in the Premier League.
Alex Oxlade-Chamberlain added a second after the half-hour mark as he scored in back-to-back top-flight matches for the first time since February 2020.
Both of those goals were created by Andrew Robertson, who now sits joint-second with team-mate Trent Alexander-Arnold (both 43) for the most assists in the league since the start of the 2017-18 season, with only Kevin De Bruyne boasting more (52).
Odsonne Edouard halved the deficit in the second half, but Fabinho secured three points with Liverpool's 169th Premier League spot-kick – the joint-most awarded to a team in the competition's history along with Manchester United.