Michael Ricketts played his first full game since returning from his loan spell with Cardiff but United conceded two goals in as many minutes to start the Red landslide.
The Reds took the lead after just 30 minutes when Dan Harding conceded a free-kick about 40-yards out, but Guiseppe Rossi smacked it passed Ian Bennett quite easily.
Frazer Campbell then made it 2-0 in a matter of seconds with a breakaway goal as he went inside Sam Hird and placed his shot inside the left hand post.
Ricketts was booked just before half-time for a foul on Spanish defender Pique.
Seconds into the second half and Leeds were three down when Rossi headed Neumayr's cross down for Campbell and the striker scored his second goal of the night.
Gavin Rothery scored the Whites' consolation on 50 minutes with a shot from the edge of the area as he and 17-year-old Howson combined.
McKeown then became the second Leeds player to be booked for a foul on Rossi.
Ricketts nearly made it 2-3 when he put in another header on goal but Lee gathered the ball safely.
Then on 84 minutes Solskjaer scored from a corner and in the third minute of extra time it was 5-1 after Simon Walton conceded a penalty when he brought Shaun Evans down from behind.
Rossi took the penalty for his second goal of the game whilst Walton received just a yellow card. Not a good night for The Whites.
Man Utd: Lee, Marsh, Kieran, Bardsley, Pique, Fox, Neumayr, Solskjaer, Campbell, Rossi, Cooper.
Subs: Howard, Heaton, Evans, Moran, Puustinen.
Leeds: Bennett, McKeown, Hird, Walton, Harding, Gray (Serrant 63), Einarsson, Rothery, Parker, Howson, Ricketts.
Subs: Vermooten, Wilberforce, Camfield, Ameobi.