Cardiff had the ideal start to the game when Crystal Palace defender Anthony Gardner headed past his own keeper to bring the teams level on aggregate at 1-1.
The Bluebirds hit the Palace woodwork three times and wasted countless chances to settle the tie in normal and extra time.
When Eagles captain Patrick McCarthy was sent off for a second yellow card on 78 minutes it seemed as if the host’s would make their dominance count, but only in extra-time they did their numerical advantage begin to count.
But Palace battled bravely in thwarting the home side and even began to look dangerous on the break but the penalty shoot-out was to prove decisive as Heaton, who had been a virtual spectator during normal play, saved from Jermaine Easter and Sean Scannell as Palace missed their first two kicks.
Referee: Howard Webb
Venue: Cardiff City Stadium
Cardiff scorers: Gardner og 7
TRIBAL ASKS: How long will Palace be able to hold on to the talented youngster Wilfried Zaha?
Yellow cards: Gunnarsson (CAR), Blake (CAR), Clyne (PAL)
Red Card: McCarthy (PAL)