Stuart Dallas sealed Leeds' place in the fourth round of the Carabao Cup as he made no mistake from the spot after James Tarkowski's miss.
Hadi Sacko opened the scoring for the visitors in the 82nd minute and sparked the game into life in the process.
Chris Wood equalised from the spot minutes later before Pablo Hernandez thought he'd snatched victory with a penalty of his own.
Robbie Brady curled a fantastic 96th minute free-kick into the top corner to take the game to extra-time.
