Carl Fletcher, Shefki Kuqi, Leon Cort and Jobi McAnuff did the damage as the Eagles threatened to run riot.
Leon McKenzie and Kevin Kyle scored what turned out to be consolations as Coventry put in a vastly improved second-half performance.
But it was too little too late as the south London side secured back-to-back victories in the league for the first time this season.
Coventry started the brighter of the two sides forcing three corners in the first seven minutes.
But it was Palace who took the lead with their first real effort on goal in the 18th minute.
The Eagles' captain Fletcher played a one-two with McAnuff before despatching a shot which flew beyond goalkeeper Luke Steele's despairing dive.
The Sky Blues almost gave an instant response as Marcus Hall delivered another excellent ball from the left, but Kyle directed his header on to the post and it bounced to safety.
Without a win since the beginning of December, the goal against the run of play clearly affected Coventry's confidence as the away side started to dominate.
Palace doubled their lead in the 26th minute as Mark Kennedy's cross was almost put into his own net by on-loan Celtic player Adam Virgo. His header was parried by Steele, but Kuqi was on hand to put the ball into an empty net.
Things went from bad to worse for Coventry as they went 3-0 down two minutes later. This time McAnuff easily beat Jay Tabb on the left before delivering an inch-perfect cross for defender Cort to head home.
With Coventry fans starting to chant "what a load of rubbish" the Sky Blues almost responded in the 36th minute as a Stephen Hughes corner was headed on to the angle of post and bar by the unlucky Kyle, with the ball rebounding into the grateful arms of keeper Scott Flinders.
But just as the home fans thought things could not get any worse - it did. This time Fletcher broke down the right and his cross was headed home by McAnuff, who beat Andrew Whing to the ball.
Coventry finally did respond in the 44th minute as Tabb fed the on-rushing McKenzie, who coolly lifted the ball over the advancing keeper.
A half-time rollicking by Sky Blues manager Micky Adams did the trick as Coventry came out firing on all cylinders in the second half.
They were rewarded in the 57th minute as McKenzie's cross found Kyle whose header this time nestled in the corner of the net.
With the fans now behind them, Coventry grew in confidence and Tabb and substitute Chris Birchall both went close with long-range efforts, but the damage had already been done in the opening 45 minutes.