Dwight Gayle, Joe Ledley and Mile Jedinak got the goals to ensure Brendan Rodgers' side, who famously let a three-goal lead slip at the ground last season in a game that derailed their Premier League title challenge, continued their poor start to the campaign.
It appeared Liverpool would exorcise the demons from last time out when Lambert, afforded a rare starting opportunity since returning to his boyhood team, converted his first goal for the club in the second minute.
But Gayle, whose double in that 3-3 draw proved so pivotal, levelled matters 15 minutes later as Palace found the ideal riposte.
Ledley and Jedinak finished the job with late strikes to heap further misery on Liverpool - whose bottom-half standing makes the lofty heights of 2013-14 seem an increasingly distant memory.
Palace, meanwhile, climbed out of the bottom three on goal difference following a first win in six league outings.
Liverpool flew out of the blocks to take the lead as Lambert, playing in place of the injured Mario Balotelli, justified his selection in the second minute.
It was the striker's connection with Adam Lallana, so fruitful at Southampton before both completed off-season moves to Anfield, that made the difference as the former picked out the 32-year-old with a lovely ball in behind Martin Kelly. Lambert did the rest expertly, deftly controlling the ball before producing the coolest of finishes.
Thoughts that an easy afternoon might ensue were quickly put to rest, however, as Gayle levelled in the 17th minute.
Yannick Bolasie was the architect, his strike at the end of a driving run rattling the post to gift Gayle a tap-in from the rebound.
The game took on an end-to-end nature thereafter, with Bolasie again threatening when forcing Simon Mignolet into a solid stop with a powerful strike from distance.
He continued to prove the biggest threat, epitomised by him forcing Dejan Lovren into a superb block at the end of a fine counter-attack.
His next chance came just before the break, Bolasie striking just over from a tight angle having collected Jason Puncheon's throughball.
Liverpool created the first chance of the second period, Martin Skrtel volleying just wide after Palace failed to clear Steven Gerrard's corner.
Yet Palace grew into the game again following that chance as they pressed forward with menace.
The hosts were unable to take advantage of good openings - something they nearly paid for when Javi Manquillo side-footed just wide from 12 yards.
Liverpool were rueing that miss almost immediately, Ledley slotting through the legs of Mignolet following more good work from the outstanding Bolasie to send the home crowd into raptures.
Hopes of a comeback were quickly snuffed out, too, as Jedinak produced a stunning 25-yard free-kick that flew into the top corner after Skrtel had brought down Gayle.
The full-time whistle confirmed Liverpool's sixth top-flight defeat of the campaign and left a rain-soaked Rodgers with plenty to contemplate.
