The Jamaica international was returning to the Eagles' starting line-up after serving a two-match ban for picking up ten bookings.
But he was dismissed by referee Steve Tanner in the 44th minute for hitting Michael Morrison in the side of his head. The home side had a lucky escape as the off-the-ball incident happened inside the penalty area - but no spot-kick was awarded.
Palace started the second half in ultra-defensive fashion, with all ten of their players sitting deep in an attempt to nullify the visitors. Yet it took only eight minutes for the Foxes, who have now lost just once in their last 11 games, to get their noses in front.
Julian Speroni saved Martyn Waghorn's shot with his legs but could do nothing to deny the lurking Berner, who stuck the loose ball into the net.
Palace had the first couple of clear chances in the game as Darren Ambrose's shot was cleared off the line by Nolberto Solano in the 13th minute and a fierce left-foot strike from Calvin Andrew forced Chris Weale into a vital save.
Leicester were getting behind the South Londoners' back four too easily and Waghorn wasted a great opportunity when he raced through, only Nathaniel Clyne's pace allowed him to get back and make a vital challenge.
Left-back Berner was proving to be the Foxes' most dangerous man and he went close with a shot which narrowly cleared the bar in the 50th minute. Moments later he made the vital breakthrough, reacting quickest to Speroni's save.
The best chance for the home team came in the 67th minute when Clint Hill's fierce header from Darren Ambrose's corner was pushed over the bar by Weale.
The Eagles continued to huff and puff in the closing stages but were unable to avoid a fifth league defeat in six matches - and they have now gone 337 minutes since their last goal and have fired blanks in their last three outings.