Against Serbian Partizan, Anthony Martial scored the only goal of the Europa League Group L game with a penalty kick after 43 minutes, but the hosts had eight strikes on target to just three by United.
The game marked the return to the ground where Matt Busby's famous team of talented youngsters played their last game, a European Cup quarter-final against Red Star in February 1958.
The plane crashed in Munich on the way home and seven United players were among the 23 who died.
United had only played in Belgrade once since then, when they lost a European Cup semi-final to Partizan in 1966.