Leon Best's seventh goal of the season secured the draw after Darren Ambrose had given the Eagles a first-half advantage.
City almost made a perfect start after a Julian Speroni mistake.
The Palace keeper spilled a simple header from defender Danny Butterfield into Michael McIndoe's path, but he couldn't get the ball out from under his feet and it was cleared.
Palace recovered from the early scare and Ambrose came close with a powerful driven shot from 25-yards but the ball went over the bar.
Ambrose was at the heart of the action again in the 20th minute, providing a good cross from Neil Danns, whose header was blocked well by the diving Keiren Westwood.
Freddie Sears pounced on the loose ball and his ball into the box nearly provided an own goal after bouncing of Aron Gunnarsson but it trickled past the post.
But it was third time lucky for Ambrose, who scored his ninth of the season in the 28th minute.
Leon Barnett's defensive header fell to Sears and he found the former Chartlon man with a low pass to the back post.
Coventry were quiet for the rest of the half but started with a bang in the second period.
McIndoe continued to torment Butterfield on the wing and turned him twice before playing a ball into the box, which Best converted with a strong header.
Coventry started to pile on the pressure and came close in the 52nd minute after another Speroni error.
The keeper dropped the ball into a crowd of players and Richard Wood was able to shoot, only for his effort to go wide.
The Sky Blues pushed for a winner but couldn't get the breakthrough they needed.