After winning the first leg at the Walkers Stadium 1-0, the Bluebirds appeared to be set for a straightforward route when they took the lead at Cardiff City Stadium.
But the visitors hit back to lead 3-2 on aggregate and it needed a Peter Whittingham penalty to take the tie to a shoot-out which Cardiff eventually won.
Cardiff's early dominance was rewarded when Jay Bothroyd flicked the ball on to Michael Chopra who fired his shot past Chris Weale in the 21st minute.
But Leicester refused to be beaten and Matty Fryatt latched on to Steve Howard's header to drive a powerful effort past David Marshall that ended up in the net despite being parried by the keeper.
The outstanding Howard then flicked the ball on for Mark Hudson to loop the ball into his own net to level the aggregate scores and the Foxes appeared to be heading to Wembley when Andy King made it 3-1 on the night in the 49th minute.
But Whittingham, scorer of the only goal in the first leg, smashed home a penalty after Alex Bruce had brought down Chopra.
No further goals were scored in extra-time and everyone had scored in the shoot-out until substitute Yann Kermorgant tried an audacious chip that was saved by Marshall.
When Marshall also saved from Martyn Waghorn the Sunderland loanee sank to his knees as Cardiff prevailed 4-3 in the shoot-out.