For Coventry, Clinton Morrison lined up against his old side for the third time since leaving at the beginning of last season.
The first half was not one for the neutral supporter as both sides struggled with the conditions and succeeded mainly in cancelling each other out for much of the play.
But it was the Eagles who enjoyed the better of the chances, with Ambrose coming close with two long range efforts early.
The first was a turn and shot from 30 yards that flew just over the bar and the second, a curling free kick from 25 yards that ended up the wrong side of the post.
The midfielder has enjoyed a rich run of scoring form lately so the near misses were not a concern as, shortly before the half hour mark he added to his tally with a close range srike.
Freddie Sears, who was up against the size and power of Richard Wood and Leon Barnett for most of the afternoon, managed to find some space inside the box for a shot.
With the angle against him he always needed to aim for the far corner, but in doing so dragged it right across the six yard box where Ambrose was waiting for a simple tap in.
The home side, who were always working against a volatile home crowd, came closest late on in the half with Aron Gunnarsson headed just wide from a corner.
But the second half was a completely different affair as both sides adapted to the wind and rain to produce a steady stream of chances.
And for Coventry that stream started with a goal as their very first effort of the half produced the equaliser.
Two minutes in winger Michael McIndoe had the space on the left flank to whip in a cross and Leon Best rose highest to convert it with a powerful header.
Minutes later they almost extended that lead when Speroni uncharacteristically missed a cross from the left. The ball fell into a melee of feet but Palace managed to scramble it wide.
Former Norwich winger David Bell saw a dipping volley fly wide on 55 when it dropped to him 18 yards out, while Sears saw his volley comfortably saved at the other end five minutes later.
Coventry continued their push for the winner and almost got it on 63 minutes with the aid of a Palace head. A free kick whipped in from the right was deflected by a Palace player and the ball skipped inches past Speroni's post.
While Morrison came even closer with the last chance of the game when his turn and shot from five yards was cleared off the line.
Coventry City : Westwood, Wright, Bell, Best, Morrison (Madine, 90), van Aanholt, Gunnarsson, Cork, McIndoe, Barnett, Wood.
Subs: Konstantopoulos, McPake, Eastwood, Cranie, Cain, Grandison.
Booked: Best, Wright.
Crystal Palace : Speroni, Hill, Derry, Fonte, Ambrose, Danns (N'Diaye, 90), Sears (John, 70), Lee (Andrew, 70), Buttefield, Ertl, Davis.
Subs: Clyne, McCarthy,Carle, Moses.
Booked: Fonte, Lee, Davis.
Referee: Jarnail Singh (Middlesex). Att:- 18200 (802 away)
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