Palace boasted two changes to the side that hit back from two goals down to draw 2-2 at Arsenal last Sunday as Vicente Guaita recovered from a groin injury to replace Wayne Hennessey in goal, while Jeffrey Schlupp came in for the injured Andros Townsend.
As expected, Leicester remained unchanged after their record-breaking 9-0 thrashing of Southampton.
Leicester had lost their previous four Premier League games against Palace, but they threatened to open the scoring in the fifth minute when Youri Tielemans played in Harvey Barnes, whose fierce strike was straight down the throat of Guaita.
Palace hit back on 10 minutes when Wilfried Zaha, on his 300th appearance for the club, skilfully put Jordan Ayew through but he blazed his effort over the top from 18 yards.
Jamie Vardy, on his 250th outing for Leicester, forced Guaita into a decent save at his front post from a tight angle on 18 minutes, before Jonny Evans met a James Maddison corner and sent a looping header just over the top.
Vardy then looked to be through on goal after a defence-splitting pass from Tielemans, but a heavy touch allowed Guaita to race off his line and gather at the forward’s feet.
At the other end, a deflected Schlupp strike from 20 yards forced keeper Kasper Schmeichel to tip the ball over his crossbar three minutes before the break.
Palace started the second half brightly and went close on 51 minutes when Cheikhou Kouyate capped off some good build-up play with a low cross into the middle where Ayew failed to convert from six yards.
Zaha kept the move alive and lashed a low strike inches wide of Schmeichel’s far corner seconds later.
Leicester responded on 56 minutes with Maddison’s corner was whipped into the middle and Evans met it with a powerful header which Guaita tipped over his crossbar.
Palace failed to take heed of that warning as Leicester took the lead from another Maddison corner a minute later when Caglar Soyuncu was left unmarked to send a stooping header past Guaita from close range for his first goal for the club.
Both sides created chances to add to the scoreline with Joel Ward cutting in from the right and hitting an effort straight at Schmeichel, before Wilfred Ndidi flashed a first-time shot from distance just wide at the other end on 74 minutes.
Vardy celebrated his milestone appearance with the killer second goal on 89 minutes as he received a return pass from Demarai Gray and drilled the ball into the net for his 10th goal of the season.
Ben Chilwell was unfortunate not to add a third during the six minutes of stoppage time when his shot from an acute angle rebounded off the far post and was cleared.
The win moves the Foxes back into third spot above Chelsea on goal difference, while Palace are down in ninth on 15 points.