Zlatan Ibrahimovic scored the second-half winner with his first goal in five matches, nodding in substitute Wayne Rooney's mis-hit shot at the far post.
It was United's first effort on target, despite dominating at Old Trafford.
Zorya offered little threat, although Sergio Romero had to be alert to save Paulinho's shot just before the winner.
Relive how Manchester United edged past Zorya Luhansk
