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.
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.
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.
The full-time whistle confirmed Liverpool's sixth top-flight defeat of the campaign and left a rain-soaked Rodgers with plenty to contemplate.
