Two penalty saves from Tom Heaton helped City to a 4th Wembley appearance since 2008.
The game finished 1 - 0 to Cardiff after 120 mins. And City won 3 - 1 on penalties as Palace failed with three of their four efforts.
Cardiff will face either Liverpool or Man City in the Carling Cup final on Sunday February 26th, ko 4:00pm.
Ticket details and allocations to follow.