Wayne Andrews gave Palace a flying start on 60 seconds and Emmerson Boyce doubled their lead 11 minutes before the break to complete an unhappy night for Micky Adams' outfit.
Coventry have now lost twice to Palace in the Championship as well as in the Carling Cup.
Coventry had their share of possession and indeed enjoyed a good 30 minutes spell where Palace keeper Gabor Kiraly had to make a couple of full length saves to deny Claus Jorgensen.
Gavin McSheffrey also lofted one over the bar and James Scowcroft fired all too tamely as the Sky Blues carved out some useful chances.
It was a positive response from the Sky Blues as they attempted to overcome a massive setback as Andrews hammered an early goal after Dougie Freedman superbly split the Coventry defence.
Andrews latched on to it like lightning and unleashed an unstoppable 20-yard shot which flew past Marton Fulop and into the roof of the net.
Palace then fell asleep and Coventry took over but the Eagles got a second, perhaps against the run of play, when midfielder Tom Soares powered his way into the penalty box before delivering a low cross into the goalmouth. It caused one hell of a scramble on the goal line before Boyce forced the ball over.
After the break Coventry kept plugging away with James Scowcroft and Michael Doyle prompting and probing in midfield. But Gabor Kiraly was rarely called upon and Palace, with Ben Watson and Freedman outstanding, again creating a few chances.
Clinton Morrison had an unlucky night and on four occasions had the keeper just to beat but got nothing for his endeavours.