Premier League Liverpool started the brighter of the two sides and went close to breaking the deadlock in the second minute. Stewart Downing cut the ball back for Glen Johnson, who curled his effort against the crossbar with Tom Heaton beaten.
However, with their first meaningful attack of the game, Cardiff took the lead. Kenny Miller threaded a pass through to Joe Mason, who took one touch before slotting the ball underneath an advancing Pepe Reina in the Liverpool goal.
Liverpool continued to dominate the tie, but were unable to draw themselves level before the break. Their best chance fell to Daniel Agger when he headed straight at Heaton from six yards out.
Cardiff had the first chance after the break, with Miller firing just wide after being found by Don Cowie.
Liverpool maintained their pressure though and eventually drew level on the hour mark. When Cardiff failed to clear Luis Suarez's shot that struck the post, centre-back Martin Skrtel was on hand to turn in the rebound.
Suarez and Downing then forced Heaton into diving saves from distance as Kenny Daglish's side seeked a winner.
The best chance fell to Championship outfit Cardiff though, when Kenny Miller turned inside the area but lashed his volleyed effort over the bar with three minutes remaining.
Liverpool started extra-time brightly and nearly found the net when Carroll's header from a corner was cleared off the line.
Substitute Craig Bellamy came close to punishing his former side, but his drive flew over.
However, it was another substitute who made Cardiff pay as Kuyt fired in at the second time of asking from the edge of the area with 12 minutes to play.
Cardiff continued to press in a frantic final few minutes and took the game to penalties when Ben Turner poked in from a corner.
Steven Gerrard, Kenny Miller and Charlie Adam were amongst those who missed their spot kicks, but it was the Anthony Gerrard, cousin of Steven, who put rhe decisive kick wide.