Antony Kay and Tommy Miller missed for Huddersfield in the shoot-out, with Lee Novack, Danny Ward and Alan Lee on target. But after former Huddersfield man Michael Flynn fluffed City's first penalty, the visitors converted the rest to secure a second shoot-out win in the competition after they beat Sheffield Wednesday by the same method in the first round.
The game ended 2-2 after normal time, with Huddersfield twice levelling to force penalties. Kay, a half-time substitute, headed into his own net from Chris Mitchell's free-kick to give Bradford the lead after 55 minutes.
The lead did not last long and in the 63rd minute Miller netted his first goal for Huddersfield from the spot after Guy Branston felled Peter Clarke in the box.
Just a minute later Bradford defender Luke Oliver powerfully headed into the roof of the net from Robbie Threlfall's corner to put them back in front.
However, Clarke tied the scores again with a swivel and a shot into the bottom left-hand corner from just inside the box that was worthy of any striker in the 70th minute.