Wade Elliott put Blues ahead shortly after the half-hour mark in the third-round replay at St Andrew's but that was as good as it got for the hosts.
Ross McCormack's first goal since September levelled matters after the break before El-Hadji Diouf quickly completed the turnaround, keeping his cool to chip home from the penalty spot after Paul Robinson had been penalised for handball - although replays suggested the crime occurred outside the area.
It means Leeds will now host Tottenham in the fourth round of the competition in a money-spinning televised clash next Sunday.
Blues boss Lee Clark did not attend the post-match press conference but it could be safely assumed he was just as frustrated with his side's cup exit as assistant manager McDermott.
"Of course we're disappointed, we're very disappointed with the second-half performance, no one more so than the manager," he said.
"It is a big disappointment because I'm sure the fans would have loved to have seen Tottenham playing here.
"We're disappointed. I think we're a bit more than disappointed actually, we're devastated really because we wanted a big game like that.
"Obviously it would have helped the club as well financially, but it's not to be.
"But, for me, the most important game is on Saturday (against Brighton) and getting three points and putting a performance on."