Richard Wood got the final touch ahead of Eagles defender Paddy McCarthy to divert a backward header past a hesitant Julian Speroni from six yards to put the hosts in the driving seat in the 34th minute.
Yet they were not firmly in control until 11 minutes from time when Marlon King converted his fifth league goal of the season.
Steffen Iversen's injury-time strike made for a frantic final few minutes but it was not to be after a finely-balanced encounter at a sunny Ricoh Arena.
Anthony Gardner headed a great chance wide for the visitors moments before Wood's opener, Wilfried Zaha was denied a solid penalty appeal while Clive Platt was repeatedly denied by Speroni at the other end.
Ultimately it was Coventry's killer instinct which proved the difference and, despite being backed by around 2,500 travelling fans, struggling Palace failed to improve on an away record which is the worst in the second tier.
City boss Aidy Boothroyd remained without the likes of skipper Lee Carsley, Sammy Clingan and Ben Turner but did welcome back influential striker King and promising centre-back Nathan Cameron to his XI.
Palace counterpart Dougie Freedman made just one change to the side who registered his first victory as Eagles boss against Middlesbrough last weekend, Owen Garvan coming in for Alex Marrow.
Sky Blues midfielder Carl Baker scored a sublime volley to help the midlands club to a 2-1 triumph over the Eagles in the FA Cup third round only last month and he was first to try his luck from 20 yards after six minutes.
Amid a lively opening quarter, Keiren Westwood was called upon to get Cameron out of jail with a solid block after he was caught in possession by Jermaine Easter in the centre circle.
With the clash having become somewhat scrappy, the clearest chance of the opening half hour went Palace's way.
Garvan's inswinging corner was missed by everyone in a light blue shirt but Gardner, at the far post, could only head into the ground and wide.
And the visitors were made to pay five minutes later.
Martin Cranie's speculative long ball forward was met by central defender Wood, who remained in the attacking third from a previous attack, and he appeared to get the final touch with a backward header from six yards.
The breakthrough owed a lot to Speroni's hesitation but he kept his side in it at the start of the second half to palm away Platt's header.
David Wright cleared Richard Keogh's attempt off the line as the hosts made a bright start to proceedings.
Palace forward Zaha saw a reasonable penalty appeal rejected having seen his shirt tugged in the area.
Platt saw two headers kept out by Speroni before King put Coventry two goals to the good as he converted Aron Gunnarsson's cross from close range.
But the home side were made to endure a frantic final five minutes after Iversen gave Palace hope from six yards.
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