The Eagles have lost only one game in five and on this form are set to be involved once again come the end of the season.
Coventry fielded new loan midfielder Lilian Nalis in a bid to end their recent poor form but they simply could not match the rampant visitors.
The opening goal came from a misunderstanding in the heart of the Coventry defence.
Palace midfielder Marco Reich recovered from an injury extremely quickly to gallop down the left flank and cross to the near post. Goalkeeper Stephen Bywater came to collect but Stephen Hughes was unaware and put the ball behind for a corner.
Coventry could not clear the flag-kick convincingly and when it fell to Danny Butterfield he tried his luck from the edge of the area. Instead it found Darren Ward who turned smartly to bury a 12-yard effort.
It was a deserved lead for the visitors who looked better in almost every department.
Iain Dowie's men could have stretched their lead just six minutes later when Tom Soares made a good break. He picked out Dougie Freedman, who looked odds on to score, but his curling shot was blocked by the flying Richard Shaw.
Coventry improved as the game went on and Ward had to show good reactions in his own penalty area to clear a dangerous free-kick from Hughes.
The respite was merely temporary and five minutes before half-time the home side restored parity. Again Hughes was involved - his curling corner was headed powerfully home by Matt Heath.
But Coventry then fell for the sucker punch. Just seconds later Butterfield landed a free-kick inside the area and Clinton Morrison pounced to put Palace back in front.
Micky Adams made a change at the break, bringing on non-contract player Youssef Sofiane who showed some useful early touches.
But there was little he could do about Palace's third - a goal which underlined the gap in class between the two sides.
The move was started by Butterfield, who picked out Morrison with a 50-yard pass. The ball flew across the face of the goal before McAnuff's centre was side-footed in by Ben Watson.
Substitute Jon Macken rubbed salt in the wounds right at the death after Claus Jorgensen had been sent off for foul language.