Steve Agnew's side had found themselves 3-0 down after 65 minutes but fought back with goals from Martin Woods and James Milner.
Leeds reject Colin Healy, making his first full start for Sunderland, broke into the box on 36 minutes to convert past keeper Martyn.
Six minutes later Black Cats trialist Clive Delaney improved his chances of a permanent move to Wearside when he arrived in the area to plant a firm header into the roof of the net.
The impressive Chris Brown added a third after the break.
Sunderland dominated for lengthy periods during the first 45 minutes and visiting keeper Michael Ingham was rarely tested.
Healy opened the Wearsiders' account when he stole into the centre to drill past Martyn after Michael Proctor and Brown had linked to set him up.
And the Black Cats were firmly in command by the 65th minute when Brown shrugged off defender Robert Constable to beat Martyn with a rasping drive.
Woods had only been on the pitch a minute when Aaron Lennon delivered a brilliant curling cross into the area which the substitute came steaming in to meet with an outstretched boot and guide the ball past Ingham in the visitors goal on 69 minutes.
Right into the last minute of normal time and Milner, who had earlier squandered a few chances to get United further back into the game, got his reward for the night when he latched onto a backpass and buried his shot into the roof of the net to his great relief.
The amazing comeback would have been complete had a fantastic run from Lennon been rewarded with the goal it rightly deserved.
The 16-year-old picked the ball up inside his own half and then embarked on a mazy 50-yard run that saw him skip past four defenders before drawing the keeper and slipping his shot past him.
Sadly the ball went inches wide of the target but would have been a remarkable goal.
Leeds ran out of time to complete the comeback, but coach Steve Agnew was pleased with what he saw from his side on the night.
"We have set standards of good play for ourselves from last week's win at West Brom," said Steve.
"For some reason though we were just a yard off tonight, particularly in the first half, and not as bright, inventive or as sharp as we have been.
"But we had already lost the services of Richardson who injured himself last night for the first team and Matthew Kilgallon, who is out on loan and we were playing against the likes of Michael Proctor who is a good player.
"The reaction we got from them after Sunderland scored their third goal was very good, they responded well to it and didn't lie down.
"So on the positive side we can look at the fact that Woods was bright when he came on and Milner emerged as an attacking force in the last twenty minutes."
Agnew also gave special praise to young defender Simon Walton, who came on for the second half and greatly impressed.
Didier Domi got a full 90 minutes of play under his belt and put in a solid performance, and must now be a serious contender to start against Middlesbrough on Saturday.
United: Martyn, McDaid, Domi, Constable, Keegan, McStay (Walton h/t), Milner, Simon Johnson (Woods 69), McMaster, Barmby, Lennon. Subs not used: Gray, Carson, Krief.
Sunderland: Ingham, Scott, Gray, Whitley, Delaney (Dickman 65), Babb, Black (Ramsden h/t), Healy, Brown, Proctor, Butler.