Cody McDonald came off the bench to secure a point for Championship strugglers Coventry.
Palace were hanging on after taking the lead through Darren Ambrose's third-minute penalty at the Ricoh Arena.
But subsitute McDonald scored from close range with 10 minutes remaining to snatch a draw.
Now unbeaten in three home games, Coventry are three points behind Nottingham Forest in 21st place with 11 games of the season left.
The hosts got off to a tricky start, with Chris Martin going down in the box under Nathan Cameron's challenge after Julian Speroni's long clearance.
Following lengthy Coventry protests, Ambrose made no mistake from the spot, beating Joe Murphy to score his seventh goal of the season.
Speroni maintained the visitors' advantage by keeping out efforts from Clive Platt and Gary McSheffrey.
Coventry were almost caught out when Cameron's weak header let in Jermaine Easter, whose shot flew over the crossbar.
But McDonald hauled Coventry level with his second goal since joining from Norwich last summer.
Coventry manager Andy Thorn:
"What I will say is the amount of dithering that went on to give the penalty, it was almost like a circus in the end.
"You have got to be 110% sure when you give a penalty. The referee went to go and ask the linesman in the end and the referee was closer, so surely if you are going to give you have got to be certain.
"I haven't seen it, so I apologise if I am wrong, but it is the way it was handled that I didn't like.
"We were edgy and nervy to begin with, but once we settled down we played some good stuff and got in some good areas and we thoroughly deserved a draw."
Crystal Palace manager Dougie Freedman:
"Overall a draw is probably the correct result because obviously I am disappointed to lose the lead in the last 10 minutes, but we have to give credit to Coventry because they showed good fighting spirit and that just might keep them up.
"The teams that are already up there in the top six are established teams that have been there for most of the season.
"The cup run has probably meant we have dropped a few points because of fatigue. That has not helped us and it has left us with a little bit of a gap from the top six.
"But we are trying. We are getting points each week - just not enough to close the gap."