Cardiff City keeper Tom Heaton proved the penalty shoot-out hero to inspire the Bluebirds to the Carling Cup final.
Heaton saved Crystal Palace's first two penalties from Jermaine Easter and Sean Scannell to book the home team's fourth trip to Wembley in as many years.
Cardiff trailed 1-0 from the first leg but Palace's Anthony Gardner headed into his own net to level the tie.
The home team then dominated but failed to turn it into goals, even when Eagles captain Patrick McCarthy was sent off.
Palace defended bravely after McCarthy's dismissal for a second yellow card on 78 minutes, holding firm during extra time.
But, having been denied by the woodwork three times, Cardiff held their nerve in the penalty shoot-out to reach their first League Cup final and book a Wembley meeting with either Liverpool or Manchester City on 26 February.
They got off to a bad start in the shoot-out when Cardiff top scorer Kenny Miller blazed his side's first kick over.
But Heaton, Cardiff's second-choice keeper who has been preferred to David Marshall throughout their Carling Cup run, turned the tide back in the home side's favour.
He brilliantly saved from Easter and then read Scannell's effort too, after Craig Conway had slotted Cardiff's second spot-kick.
Rudy Gestede and Peter Whittingham put Cardiff 3-1 ahead, either side of Mile Jedinak firing into Heaton's bottom right corner to get Palace going.
But Jonathan Parr's nerve failed him, as he too missed the target to ensure that a tense all-Championship semi-final between Malky Mackay's third-placed Cardiff and Dougie Freedman's 14th-placed Palace went to form.
Having started with attacking intent, Cardiff levelled the tie after just seven minutes.
Darcy Blake played the ball into the right channel for the onrushing Don Cowie, the Scottish midfielder wrapped his foot around the ball to send in a dangerous cross and Gardner, Palace's goal hero from the first leg, instinctively lunged at the ball but headed into his own net.
Palace keeper Julian Speroni then beat away a fierce shot from Whittingham, before Aron Gunnarsson ballooned a header over and Miller slid just wide before going even closer in time added on at the end of the first half, controlling with his back to goal at the edge of the area before spinning in one fluid movement to crash a left-foot shot against the post.
Palace came out hard after the break but it was the same story, Whittingham again firing wide before bringing the best out of Speroni, who tipped over his free-kick.
McCarthy then came to the Eagles' rescue moments later, clearing off the line when Anthony Gerrard peeled away to head a free-kick past Speroni.
But the Palace skipper was to get his marching orders 12 minutes from the end of normal time when he scythed through the back of Miller, his second yellow card, having already been booked for an earlier foul on the same player.
Cowie had a late chance to win it in normal time before being sacrificed when Mackay opted to take advantage of the extra man.
He brought on another attacker in Gestede, who laid the ball off perfectly in the second period of extra time for Filip Kiss, only for the Slovakian midfielder to clip the top of the bar with his rising shot.
Then came the best chance to avoid going to penalties when Gunnarsson lost his marker but, from four yards out, he somehow contrived to head against the bar with the net gaping.
Heaton had the final word, however, to ensure that Cardiff would not regret all their missed chances, allowing the Welsh side to go through to contest their third major Wembley final in five years.