Fabio Borini hit a stunning strike to level the game and grab a crucial point for Sunderland.
Dame N’Doye’s deflected first-half effort had put the hosts in front.
Connor Wickham scored twice in six second-half minutes against his former club to put Palace on course for a first league win in 11 games.
But substitute Borini’s injury-time effort from an almost impossible angle rescued a point for Sam Allardyce’s side and moved them up to 17th.
Sunderland are only out of the drop zone on goal difference, with Norwich and Newcastle also on 24 points and occupying the two places below them.
But, having been faltering in the bottom three since November, this late show will give Allardyce confidence that his men have the stomach for a relegation fight.
The Black Cats still only have one win in seven though, and their frailties were on show when they almost collapsed just after the hour mark, as Wickham snatched two well-taken goals.