Cameroon international Eric Djembe-Djembe hit a dubious 117th minute winner with a half-volley from 15 yards after Leeds failed to clear a corner.
Brazilian World Cup winner Roque Junior answered his critics by heading Leeds into a 49th minute lead, but David Bellion sent the game into extra time by grabbing a 78th minute equaliser, darting into the penalty box and shooting through Paul Robinson's legs.
It needed an instinctive save from Paul Robinson to spare Junior the embarrassment of conceding an own goal just before the end of normal time.
But after Diego Forlan had put the visitors ahead for the first time in the 108th minute when looking suspiciously offside at the far post, Junior struck again five minutes later, the ball going in off his knee.
With a penalty shoot-out looking likely, Djembe-Djembe struck his winner into the turf and just under the bar.
Ironically, Sir Alex Ferguson's priorities clearly lay elsewhere. He sent out a much changed Manchester United side which included seven players who failed to make the starting line-up when the teams met in the Premiership ten days earlier.
Robinson swooped on Diego Forlan's angled shot in the Reds' only menacing attack of the opening 45 minutes.
Seth Johnson livened things up immediately after the interval by unleashing a left foot shot which Carroll could only parry and Smith struck the rebound into the net only to be flagged offside. Obviously interfering with play!
Leeds, however, took the lead when Johnson sent over a corner from the right and Junior rose high in the goalmouth to head his first goal for the club.
Bellion had a goal disallowed for offside when he pounced at the far post but there was no flag the next time he beat Robinson with that 'nut-megged' goal - also his first for the club.