After referee Howard Webb had reversed a decision to award Palace a second-half penalty at Selhurst Park, Jason Puncheon fired the ball in off the post following fine work from Yannick Bolasie.
Puncheon's 76th-minute strike, his third goal in two games, ensured Palace's impressive revival under Tony Pulis continued.
The result leaves the London club, who have kept four clean sheets in their last five matches, seven points clear of the relegation zone.
Villa, meanwhile, have lost four straight games and now sit just four points above third-bottom Fulham.
Lambert welcomed back Karim El Ahmadi, Fabian Delph and Gabriel Agbonlahor following injuries, while Ciaran Clark was also recalled.
Pulis named an unchanged team but, after Kagisho Dikgacoi went off injured, he was forced into an early substitution, sending on Marouane Chamakh and reverting from a 4-5-1 formation to 4-4-2.
Almost immediately, Chamakh's strike partner, Cameron Jerome, hacked Agbonlahor's downward header off the Palace goalline.
Then, following neat build-up play from Delph and Grant Holt, Damien Delaney flung himself in the way of Ashley Westwood's piledriver to make a decisive block.
In the 36th minute, Palace created a great opportunity with a cleverly worked free-kick. Mile Jedinak shaped to shoot but instead gave the ball to Puncheon, who slid the ball through for Bolasie inside the area.
Bolasie claimed to have been impeded by Holt as he looked to shoot, but as the ball drifted wide the referee waved away Palace's penalty appeals.
Four minutes after the restart, Agbonlahor tried his luck from the edge of the box, but Julian Speroni made a comfortable save.
Jerome then missed a glaring chance to score only his second goal in 26 Premier League games this season. Bolasie tricked Matthew Lowton with step-overs and unleashed a shot, which Brad Guzan blocked. The ball fell to Jerome, unmarked at the back post, but with the net unguarded he fired the ball against the crossbar.
The lively Bolasie's low drive from the edge of the box went just wide on the hour as Palace ramped up the pressure.
Webb pointed to the spot in the 68th minute when the Palace players appealed for handball against Clark, but changed his mind after talking to one of his assistants.
Bolasie then sprinted down the left and provided a fine cross for Puncheon, who controlled the ball neatly, swivelled and fired a low shot home.
Puncheon hit the bar after a quick counter-attack, but Palace had Speroni to thank for keeping all three points.
In the 88th minute, the in-form Argentinian goalkeeper, who turns 35 next month, made a superb save to deny Andreas Weimann from close range, leaving Villa to reflect on an increasingly perilous position in the table.
