The Eagles went into Tuesday night's game hoping to put distance between themselves and 22nd-placed Scunthorpe but Leicester deservedly claimed back-to-back league victories and have now just lost one in 11 league games.
The turning point of the match was the first-half sending-off of Claude Davis, who was dismissed for violent conduct in an off-the-ball incident with Martyn Waghorn.
The Foxes were also indebted to Chris Weale who made several fine saves.
Paul Hart's Palace men started poorly by giving the ball away several times in midfield, with Neil Danns particularly culpable on his 150th league career start.
They were nearly punished when Leicester launched an attack following a Palace mistake, but Andy King missed the target with a fifth-minute header.
Paul Gallacher should have given Nigel Pearson's men the lead three minutes later when he beat the offside trap, but he fired wide when through on goal.
Davis, who was returning to the Palace squad following a two-match suspension, was then lucky to receive just a booking after he made a rash two-footed challenge on Andy King.
Following a lull where neither side managed to create any chances, both goalkeepers were called into action in quick succession.
First, Calvin Andrew's snap shot produced a fine save from Weale in the 28th minute.
From the resulting corner, Leicester launched a counter-attack and Matt Oakley's strike from just outside the area required a magnificent save from Julian Speroni.
On the stroke of half-time, the hosts were reduced to 10 men as Davis was ordered off.
However, Berner, who found himself in acres of space lashed a shot from the edge of the area over in the 50th minute.
The full-back made amends three minutes later when he followed up Waghorn's shot, which could only be parried by Speroni, and smashed home.
It began to look ominous for Palace as their opponents have not lost a game in which they have scored the opening goal.
That did not deter Danns though and his shot on the hour mark was well saved by Weale.
Gallagher, who scored both goals in Leicester's 2-0 win over Palace in the reverse fixture, nearly doubled the lead but his 20-yard volley was magnificently tipped round the post by Speroni.
Clint Hill's 67th-minute header from Darren Ambrose's corner looked to be heading for the top corner, however the impressive Weale made yet another superb save.
Leicester controlled possession thereafter although they failed to create any meaningful chances as Palace battled in vain to find an equaliser.