The Reds moved six points clear at the top of the Premier League table and ensured they’d be sitting at the summit on Christmas Day as they hit top gear in London.
Takumi Minamino set them on their way inside three minutes when he swept in a first league goal for the champions.
Sublime strikes from Sadio Mane and Roberto Firmino followed before the interval, though Palace created a handful of opportunities which they were unable to capitalise on.
Liverpool showed no let-up after the break as Jordan Henderson rasped in a fourth before Firmino clinically added goal number five.
Mohamed Salah came off the bench to round off the scoring with a close-range header followed by a magnificent curling effort to make it seven and also provided an assist.
“We dealt the whole season already only with the circumstances – with the injuries and stuff like this, you cannot prepare, you just have to sort these kind of problems.
“We all know, we had a lot of problems and when one started it just leads to the next problem and that means you have a player less at centre-half and then another one has to play seven times in a row because nobody else was fit and the young kids were not ready and all these kind of things.
“It doesn’t stop. In the moment, it’s just one hour after the game where we think it’s fine – but from tomorrow on we try to prepare for all the different scenarios again and do what we have to do to make sure we will win football games in the end of December.
“It’s just tough and nothing to be satisfied or whatever.”