Substitute Gary McSheffrey, on the pitch for just three minutes took advantage of an Alex Kolinko mistake to fire the Sky Blues in front on 68 minutes. but the Eagles' Nigerian striker, who has been out injured since the end of last season, replied with a superb header 18 minutes from the end.
An ordinary first half saw both defences in control although the Eagles went close to scoring in the opening minutes when Dele Adebola and Tommy Black both went for the same header and allowed Morton Hyldgaard to turn the effort past the post.
Julian Gray then shot wide of the target before Kolinko made a good save from Dean Gordon at the other end.
The second half was brought to life when a deep cross from Gary Caldwell was spilled by Kolinko and McSheffrey was well placed ten yards out to fire into the empty net.
The goal was against the run of play but the lead lasted just five minutes for Gary McAllister's boys.
Substitute Wayne Routledge found Black in space on the right and his perfect cross was met brilliantly by Akinbiyi, who headed powerfully past Hyldgaard.
The Palace hitman could have clinched all three points near the end but the Danish keeper made a crucial stop to ensure the spoils were shared.