Johnny Evans scored his first goal for Manchester United and Giuseppe Rossi also scored a penalty as the away side came back from their home defeat to Sunderland last week.
Gerard Pique also had a header beat Neil Sullivan but onto the post when Rui Marques, playing right-back, was harshly adjudged to have fouled Lee Martin inside the area after just 11 minutes. Rossi converted the kick for his second goal of the season, sending Sullivan the other way.
17-year-old Evans scored the second 11 minutes later as he headed home Markus Neumayr's corner.
Sullivan had made an early save from Rossi who managed to turn on the edge of the area.
Marques tried an attempt from all of 25-yards which had Lee struggling to keep the ball out.
Sullivan also made two fine saves from Martin and Cooper, preventing the scoreline being any worse.
Ian Moore also had a header cleared off the line from a Danny Pugh flag kick in what was a disappointing curtain raiser for the reserves at Elland Road.
Leeds: Sullivan, Marques, Kilgallon, Walton, Crainey, Gray (Gardner 56), Bayly (Madden h/t), Wright, Pugh (Morris 75), Blake, Moore.
Subs Not Used: Wilberforce, Howson,
Man Utd: Lee, Simpson (Shawcross 88), Pique, J Evans, Bardsley, R Jones, Neumayr, Gibson, Martin (S Evans 88), Cooper (Blake 74), Rossi.
Subs Not Used: Zieler, Rose.