Cardiff City are to march on Wembley again. A pulsating semi-final was claimed from Crystal Palace's 10 men on penalties, victory secured courtesy of Tom Heaton's two saves in the shoot-out and another effort skewed wide by Jonathan Parr. The last miss prompted a pitch invasion from the jubilant home support while the goalkeeper tore upfield in celebration and visitors sank to the turf, players lost in delight and despair amid the fans.

The home side would argue that anything other than passage to a first League Cup final would have been a travesty. While Palace's resilience and sheer, stubborn refusal to wilt was hugely admirable and worthy of praise, their woodwork had been rattled three times over the course of the 120 minutes. The bar shivered twice in the second period of extra-time alone, Filip Kiss's volley clipping the angle and Aron Gunnarsson somehow contriving to thump a free header against the timber as the clock ticked into the last minute.

The frustration that generated was lanced in the shoot-out, with Palace's more regular penalty takers long since substituted and their players finally succumbing to the emotion of the evening.

Heaton, second-choice in the Championship but used throughout the Carling Cup run, blocked weak attempts from Jermaine Easter and Sean Scannell, and Palace were blunted – Kenny Miller's earlier miss no longer relevant – fatigue having anchored the visitors at the last. "Maybe the physical output we'd put in with 10 caught up with us," said Palace's manager Dougie Freedman. "We were out on our feet, and maybe struggled to compose ourselves." Parr's effort sealed their fate.

They had been fighting a rearguard action ever since Paddy McCarthy's dismissal for two fouls on Miller, both clumsy and meriting of sanction, the red card brandished 12 minutes from the end of normal time. The huff and puff that followed somehow kept Cardiff out, but fate was against Palace. Both managers justifiably spoke of pride in their own, but this was to be a night for this pocket of south Wales to savour.

Cardiff have grown used to trips to the national stadium in recent years, and next month's will be their fourth trip in as many years. Yet it feels more timely than most. This club have rather shivered in the shadow of Swansea's stylish ascent into the top-flight, but this will offer the Bluebirds their own chance to flourish. Either Manchester City or Liverpool await. Malky Mackay was unwilling to contemplate either yet. "You'll be asking me who I want in the first [Europa League] group game next," he quipped. Is he looking forward to the final, though? "Just a wee bit …"

His team will have to eradicate the profligacy that blighted them in both legs of this tie if they are to damage that calibre of opposition. Palace's Anthony Gardner scored both goals in the semi-final, his winner at Selhurst Park a fortnight ago nullified by an own goal that levelled the contest on aggregate.

City had snapped into challenges from the outset, their midfield a blur of tackles to disrupt Palace's attempts to settle. Parity was established when Darcy Blake slipped Don Cowie to the byline, with the winger's cross converted by the visiting centre-half.

That might have opened the floodgates, the excellent Peter Whittingham testing Julián Speroni from distance and Miller twice spurning chances just before the interval. The Scot skimmed one wide of the far post having been sent through by Gunnarsson. And the half-volley spat viciously against the other post right at the end of the first period was magnificently executed but had the locals cursing in disbelief.

Yet Palace, for all the slippery running and trickery of Wilfried Zaha, would not muster an effort on target until the shoot-out. They might have earned a penalty when Gunnarsson dragged down Chris Martin, but their threat was only ever on the counter-attack and was invariably snuffed out. They certainly offered more poise as the contest progressed, but McCarthy's dismissal undermined that just as momentum was building.

Thereafter it was merely about blanket defence with composure draining, cruelly, after the final whistle. The Londoners' crowning glory in the cup run came in eliminating Manchester United at Old Trafford in the quarter-final – Cardiff will hope theirs is yet to come.