But Palace could not find a way through a determined defence and had to settle for a share of the spoils at the Liberty Stadium.
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 Serran brought down Danns as the midfielder burst through.
Serran and his team-mates pleaded his innocence but referee Anthony Taylor brandished a straight red card.
Swans boss Paulo Sousa sacrificed midfielder Joe Allen for defender and club captain Garry Monk, back in the squad after injury.
Palace immediately went on the attack and Danns sent a header wide before Calvin Andrew, still looking for his first goal since signing from Luton last summer, nodded Darren Ambrose's free-kick over.
Austrian midfielder Johnny Ertl tried his luck from long range but Swans keeper Dorus De Vries was not unduly troubled.
After the break a cross from Nathanial Clyne caused minor panic in the Swansea area but the the home defence managed to block shots from Ambrose and Victor Moses before Danns fired the loose ball wide.
Eagles boss Neil Warnock turned to former Cardiff striker Alan Lee in place of Andrew in a bid to break the deadlock.
Teenage winger Moses, who is expected to leave for a Premier League side when the transfer window opens next month, almost gave the Palace fans something special to remember him by with a stunning run past three Swansea defenders, but Lee could not get a head on his cross.
Moses departed the action soon after to be replaced by Freddie Sears, who is set to be recalled by West Ham next week.
Sears, who has not managed a single goal since joining the Eagles on loan in August, spurned a great chance when he raced through only to shoot too close to De Vries while Ambrose was screaming for a pass.
At the other end Andrea Orlandi was fed by Nathan Dyer on the break but his shot was saved by Speroni to ensure honours ended even.