Neil Warnock's side were by far the better side as Coventry, who had tasted victory at Birmingham City on Monday night, failed to build on their win.
Chris Coleman named the same side which had won at St Andrew's but the performance could not have been more different.
Palace were superior in every department but were especially dominant in midfield where the highly-rated Ben Watson was in complete control.
Neither side had settled into any form of rhythm before Palace went in front in the ninth minute.
Jose Fonte headed down a free-kick and when the ball hit the Coventry post, Clint Hill was on hand to turn it in.
It was a bad start for Coventry but it never really got any better. Watson had the better of Aron Gunnarsson and Guillaume Beuzelin and was able dictate the pace of the game.
Palace did not create that many chances but didn't really need to.
Coventry did get the ball in the net four minutes from the interval when Michael Mifsud headed the ball towards goal.
It looked to be heading for goal but when striker Clinton Morrison made sure but he was flagged offside.
Coleman will have expected more in the second half but did not get it and, as a former defender, will not have been happy with the away side's second.
Watson's 25-yard free-kick went through the defensive wall and was diverted in past Keiren Westwood.
Coleman made his changes early but it made precious little difference.
Robbie Simpson went close in final minute when he curled a free-kick just over the bar.