The ball found its way into the net in less than 30 seconds after Ismaila Sarr slipped past Kostas Tsimikas and delivered a precise pass to Eddie Nketiah, who expertly placed the ball past the goalkeeper. However, the goal was disallowed as Nketiah was deemed offside.
The hosts started the game sharply but Liverpool took the lead with their first real attack in the ninth minute when Cody Gakpo ran on to Tsimikas' through ball down the left.
He centred for Jota, who breezed past Palace debutant Trevor Chalobah to poke home from close range and record his fourth goal of the season in all competitions.
Jota should have doubled his tally in the 34th minute after good work by Mohamed Salah and the impressive Ryan Gravenberch, whose ball from the right found Jota unmarked but he scuffed his effort well wide.
Liverpool enjoyed almost 75 per cent possession in the first half but without creating many clear-cut chances and Palace almost made them pay on the stroke of half-time.
Maxence Lacroix's quick pass played Ismaila Sarr in behind, but his low effort was well saved by Alisson.
The second half began quietly before the visitors began to move through the gears and Salah drew a smart block from Palace keeper Dean Henderson after cushioning down a wonderful pass from Virgil van Dijk.
Jota missed another good chance just after the hour when Trent Alexander-Arnold found him in space from a free kick, but the Portugal forward mistimed his header.
Liverpool's failure to kill the game almost cost them as Eddie Nketiah and Eberechi Eze drew good saves from Alisson, who went off injured after he was forced into a hasty clearance.
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That brought Vitezslav Jaros on for his Liverpool debut with the Palace fans sensing a shift in momentum, but Eze shot straight at Jaros who also stopped substitute Jean-Philippe Mateta in his tracks in added time.
Liverpool stay top with 18 points from seven games and open up a four-point lead on Manchester City and Arsenal, who play later on Saturday.
"I think it's always hard to come here. The results over the years have all been very tight and close," said man of the match Van Dijk. "We could have played a bit better in the second half. Overall, it's a big three points and we go into the international break on a high."
Palace remain winless with three points from seven league games.
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