'It looked a little bit like childish football...then we scored' - Jurgen Klopp
Goals from Emre Can, Dejan Lovren, Joel Matip and Roberto Firmino earned Liverpool victory as they stretched their unbeaten run to 11 games in all competitions to remain level on points with Manchester City and Arsenal at the top of the Premier League.
Palace midfielder James McArthur had twice levelled for the hosts with headed goals.
Liverpool boss Jurgen Klopp was pleased with some aspects of his team's display but felt there was still room for improvement.
"What can I say? The first 15 minutes I was not too happy, it looked a little bit like childish football; very good but no greed, no direction," he said.
"Then we scored and we started playing football and I'm not sure that we played a lot of times better than we played then offensive-wise.
"After half an hour, we created chance after chance after chance, scored not often enough but we scored and then we opened the game by ourselves again.
"(It was a) close game; a deserved win at the end and I'm very happy in the moment."
Alan Pardew questioned the decision to appoint Andre Marriner as referee for Crystal Palace's 4-2 defeat to Liverpool.
Marriner awarded Liverpool a contentious last-minute penalty in the same fixture last season, which was converted by striker Christian Benteke - who has since moved between the two clubs - to give the Reds a 2-1 success.
The official was booed by sections of the Selhurst Park crowd during Saturday's game and Pardew was also frustrated Marriner turned down three penalty appeals from the Eagles.
Pardew told BT Sport: "It was too open at times for us and we gifted possession a little bit too much to Liverpool.
"But there were still some decisions that went against us today. I don't think Andre Marriner should have reffed this game. He gives the penalty last year so we've got a negative in our mind anyway.
"Why was Mike Riley (manager of the Professional Game Match Officials) giving him the game today? I can't understand it.
"And then we get three penalty calls, okay they are tight but they are probably no worse than Christian's last year so it's just a little bit frustrating that part.
"Having said that, Liverpool are a bloody good team and we found it difficult at times."