Swansea made the brighter start with Palace keeper Julian Speroni forced to palm a long-range shot from Gorka Pintado onto a post.
But the hosts’ game plan was thrown into disarray in the 17th minute when Albert Serran brought down Neil Danns as the midfielder burst through and ref Anthony Taylor brandished a straight red card.
Swans boss Paulo Sousa sacrificed midfielder Joe Allen for defender Garry Monk.
Palace went on the attack and Danns sent a header wide before Calvin Andrew nodded Darren Ambrose’s free-kick over.
After the break Palace sub Freddie Sears raced through only to shoot too close to Dorus De Vries while Ambrose was screaming for a pass as the honours ended even.