Leicester travelled to South Wales a goal down from the first leg and were two goals down on aggregate when Michael Chopra scored in the 21st minute.
Matty Fryatt made it 1-1 on the night four minutes later and a 36th minute Mark Hudson own goal had the Foxes ahead at the break.
Andy King made it 3-1 in the 49th minute but a 69th minute Peter Whittingham penalty meant that the game went to extra time.
That failed to produce a goal so penalties was required. Cardiff won those
4-3 to book their place in the Wembley final on May 22nd against Blackpool who beat Nottingham Forest last night.