The game, which took place at the Selhurst Park stadium in London, ended with a score of 3: 1 in favor of the Merseyside team.
Virgil van Dijk (8'), Alex Oxlade-Chamberlain (32'), Fabinho (89', penalty) scored for Liverpool.
The London team scored Odsonne Edward (55').
Liverpool are second in the Premier League with 48 points.
Crystal Palace (24) is in 13th position.
Leader in the Manchester City Championship (57).
Earlier it was reported that Manchester City interrupted the 12-match winning streak in the Premier League.