Bradford boss Phil Parkinson was pleased with his side's patience in their
Goals from Billy Knott and James Hanson secured a place in the third round and an away tie with League One rivals MK Dons, who beat Manchester United 4-0.
Parkinson told BBC Radio Leeds: "It was a cracking night of football. We were patient, and a moment of inspiration from Billy got us back in it.
"We had to raise our game because Leeds are a decent side, and I felt we did."
The two clubs have had contrasting starts to their league seasons, with Dave Hockaday's side losing three of their four Championship games and Bradford taking seven points from 12 in League One.
But Parkinson's side fell behind in the 82nd minute, despite Leeds having Luke Murphy sent off early in the second half.
Knott fired home from 25 yards soon after before Hanson - a hero in the Bantams' - headed the winner.
"At Bradford City you never know you're beaten," added Parkinson.
"Billy's got those big moments in him and I thought he was magnificent throughout.
"Now we'll go to Milton Keynes and I'm not greedy, we had a glamour tie with Leeds so we won't let not getting a big draw take the gloss off."