Defoe completed a remarkable comeback with his third goal two minutes from time to earn praise from caretaker manager Trevor Brooking.
"He is a smashing lad and it was a great hat-trick," he said after the game.
"To come back like this after being sent off at the weekend shows great character and I'm very pleased for him.
"We had a little chat on Saturday and I told him that if he wants to get at his opponents all you need to do is put the ball in the net and tonight he has done just that."
Cardiff started like a house on fire and Robert Earnshaw opened the scoring in the 12th minute with a close-range strike.
Midway through the half he was on target again when he curled a superb shot beyond the reach of England keeper David James.
Referee Andy D'Urso gave the Hammers a lifeline when he awarded them a controversial penalty a minute before the interval which Defoe gratefully rammed into the net.
"That was definitely the turning point in the game," said Earnshaw.
"Up to then we had been playing good football and got the goals we deserved but in the second half we didn't do as well."
Brooking's plan of using three strikers began to pay dividends and Defoe levelled in the 63rd minute with a shot that needed a slight deflection before beating home keeper Martyn Margetson.
Just as extra time was beckoning Defoe popped up to fire through a crowded goalmouth and put the Hammers through to round three.
"The penalty was unfortunate and if we had come in 2-0 at the interval it could have been different," said Bluebirds boss Lennie Lawrence.
"We kept them apart in the first half but we have now conceded so many second-half goals that something has to be done about it.
"I will have a look at the tapes tomorrow and must come up with some answers."
Cardiff: Margetson, Weston, Gabbidon, Vidmar, Barker, Boland, Kavanagh, Bowen, Bonner, Thorne, Earnshaw. Subs: Alexander, Prior, Campbell, Croft, Gordon.
West Ham: James, Repka, Dailly, Pearce, Ferdinand, Quinn, Etherington, Horlock, Connolly, Defoe, Mellor. Subs: Sofiane, Garcia, Kilgallon, Noble, Bywater.
Referee: A D'Urso (Essex).