Johnny Evans scored his first goal for United and Giuseppe Rossi also scored a penalty.
Gerard Pique also had a header beat Leeds goalie 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.
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.