Second half goals from Andrew Johnson and Jacob Berkeley gave Palace maximum points from their trip to the Midlands.
Gary Issott named Johnson, Barry Bannan and Peter Ramage in an experienced starting eleven and after soaking up first half pressure from the home side Palace did have chances of their own to break the deadlock.
In the seventh minute, Palace had their first chance of the game when Johnson's low shot was blocked by Cian Harries and from the resulting corner, Sullay Kaikai just failed with his effort from the back-post.
Goalkeeper Lee Burge kept his side on level terms just before the break when he denied Jake Gray with a good save from the striker’s powerful shot. The sides went into the break with the deadlock still not broken.
At the start of the second period the home side had an opportunity to go ahead when Dion Kelly-Evans found himself in space in the box but he put his chance over the bar.
Twenty two minutes into the half the visitors did get the advantage when a long ball upfield was picked up by Johnson and he made no mistake as he put the ball past Burge to give his side the lead.
The Sky-Blues had a chance to get back on level terms soon after as the young side had a free kick from distance. Lewis Price tipped the ball over the bar as James Maddison saw his shot from fully 25 yards put out for a corner and it was not long before the win was confirmed.
Issott sent on substitute Fisayo Adarabioyo with ten minutes remaining and he beat the offside trap to get his shot in on goal but that was blocked and it fell to Jacob Berkeley who finished off the move for the Eagles to pick up a victory on the road.
Coventry City: Burge, Whitmore, Di. Kelly-Evans, Finch, Lawton, Harries, Maddison, Stevenson, Thomas, Spence (Sambou 74), Coulibaly (Kelly-Evans 64).
Subs not used: Addai, Maycock.
Crystal Palace: Price, Egbo, Berkeley, Boateng, Inniss, Ramage (Magri 46), Gray, Dymond (C), Johnson (De Silva 80), Bannan (Adarabioyo 80), Kaikai
Subs not used: Pain, Allassani.