They showed two changes in midfield from the side that drew at Reading with Joe Allen and Thomas Butler starting in place of Andrea Orlandi and Nathan Dyer, who were both on the bench.
A third minute corner by Butler led to an opening for Allen but he fired well over before forcing another corner that was cleared by Eagles skipper Shaun Derry.
The Swans kept up the pressure and Gorka Pintado struck a swerving shot that visitors keeper Julian Speroni turned on to a post before scrambling to safety.
The home side were reduced to ten men when referee Anthony Taylor sent off Serran after the defender challenged Neil Danns. The Palace midfielder had made a run towards the home goal when he fell under Serran's challenge.
The referee decided that he was clean through on goal and showed the Swansea player a red card much to everyone's amazement.
Gary Monk replaced Allen who had been booked in the 20th minute as Paulo Sousa's men regrouped with Alan Tate switching to full-back.
They held out for the remainder of the half, but with Darren Pratley closely marked by Palace's Johannes Ertl the home midfield found it difficult to keep hold of the ball.
Pintado was yellow carded in the 46th minute along with Palace's Clint Hill as the Swans made a positive start to the second period.
The visitors made a change up front on the hour with former Cardiff striker Alan Lee replacing the ineffective Calvin Andrew. This was quickly followed two minutes later by Dyer taking over from Cedric van der Gun for the Swans.
The introduction of Lee caused the Swansea defence a few problems, but he was unable to make anything of a couple of headed opportunities.
Freddie Sears should have snatched all three points for Palace seven minutes from time, but Dorus de Vries came out to smother his close-range shot and the danger was cleared.