Eoin Doyle headed the visitors into a shock 19th-minute lead at Elland Road but Michael Brown levelled in the 28th minute and Dominic Poleon grabbed what proved to be the winner four minutes later.
Nathan Smith almost equalised in the fifth minute of injury time but his shot hit a post as Leeds hung on to edge the match 2-1.
League One Notts County also had to come from behind to defeat Fleetwood 3-2.
The League Two side went ahead through Gareth Evans in the 16th minute but County led at the break thanks to goals from Enoch Showunmi (28) and Danny Haynes (40).
Callum McGregor looked to have made the game safe when he added a third for the hosts in the 73rd minute but Manny Smith was red-carded 10 minutes later after picking up a second yellow and David Ball pulled a goal back for Fleetwood two minutes from time.
The game of the night saw Carlisle upset Blackburn with a 4-3 penalty shootout win after a 3-3 draw at Brunton Park.
Rovers looked the more likely winners for much of the game, leading 2-1 and 3-2 and then 3-1 on penalties.
But Chris Taylor and Josh Morris missed with successive efforts and David Symington scored the decisive penalty for Carlisle.
It had been 2-2 at the end of normal time, with David Amoo giving Carlisle a first-half lead before the game burst into life just after half-time.
Tom Cairney equalised in the 52nd minute then David Dunn missed a penalty for Blackburn two minutes later. Two minutes after that Taylor did put the visitors ahead but Lewis Guy levelled things up in the 62nd minute.
Alan Judge became the third player on the night to score his first goal for Rovers in the 95th minute but on-loan Hull midfielder Cairney was sent off five minutes later and Amoo made it 3-3 in the 114th minute.