Liverpool began in fine style and took the lead just 14 minutes in when Luis Suarez managed to sweep the ball home from 12 yards despite being surrounded by defenders.
Just moments later and Daniel Sturridge kept up his brilliant start to the new season when firing home after turning Damien Delaney inside-out.
The third, just before the break, was somewhat harsh on Palace as Dean Moxey was adjudged to have pulled Raheem Sterling back just inside the back and skipper Steven Gerrard made no mistake to slot him his 99th Premier League goal for Liverpool.
Palace did improve after the break and they claimed a goal with 15 minutes left as Dwight Gayle flicked home Jose Campana's free-kick from close-range - but it proved to be nothing more than a consolation.
The win takes Liverpool above Arsenal into top spot, whilst Palace remain second from bottom after their sixth defeat of the season.
The match again underlined the fact that Liverpool now possess one of the most dangerous front-lines anywhere in Europe.
Individually their statistics are formidable, together they are devastating. Suarez has 19 goals in his last 22 games, while Sturridge has 19 in 24 games since joining in January, including eight in nine matches this season.
Sturridge's form would seem to make him a certain starter for England's important World Cup qualifying double-header next week - injury permitting.
Sturridge was watched by England coach Roy Hodgson, who had dashed down the M62 after watching Manchester City's earlier victory over Everton.
Liverpool were up and running after 14 minutes when Victor Moses's cross-field run delivered the ball to Suarez who instinctively rolled it into the path of the overlapping Jose Enrique.
The Spaniard knew exactly what to do, getting to the byline and cutting back to Suarez, who improvised brilliantly as he fell to the ground under pressure from Jason Puncheon, hooking the ball home while on his way down on one knee.
Within three minutes Liverpool had doubled their lead, with Suarez and Enrique playing a minor part this time.
The Reds left-back tried to pick out the Uruguayan with a long pass out of defence and, with Adrian Mariappa coming out to challenge, the ball went over their heads and put Sturridge in one-on-one with Delaney in the inside-left channel.
Sturridge changed direction three times on his way into the penalty area, leaving his marker all at sea, with the final switch giving the England striker just enough room to fire an angled shot across Julian Speroni and inside the far post.
The Enrique, Suarez, Sturridge triumvirate was in overdrive as another incisive move cut open Palace and only the outstretched foot of Delaney prevented Sturridge sliding home.
Even when Mamadou Sakho and Martin Skrtel took each other out going for the same ball to put Jimmy Kebe through, Kolo Toure swept up in to prevent the first shot going in and goalkeeper Simon Mignolet saved Puncheon's follow-up.
Sakho's good fortune continued when he sliced just wide of his own post after Mignolet failed to deal with low left-wing cross.
The match was over as a contest in the 38th minute as Moxey's was blown for pulling on Sterling, which was spotted by assistant referee Richard West. Referee Anthony Taylor pointed to the spot and Gerrard stroked home.
Palace had a better second half and were eventually rewarded with a goal after taking advantage of Liverpool's frailties at set-pieces.
Half-time substitutes Campana and Gayle combined with the former curling in a free-kick from out wide on the left and the latter touching it in.
Sturridge could have had his second when he hit a post late on and England will hope he can carry that form on to the international stage.