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Ole Gunnar Solskjaer's United knew that a third victory in four Group L against Serbian Partizan would be enough to send them through.
The 18-year-old Greenwood broke the deadlock in the 22nd minute with a cool finish to score his third goal of the season and second in this competition.
Anthony Martial doubled the advantage after the half-hour mark with a brilliant individual goal, before Marcus Rashford lashed home the third four minutes after the interval.
The comfortable victory saw United bounce back after a 1-0 loss at Bournemouth last weekend had ended a three-game winning run.
"I think it was a good performance but there are things we can improve on," Rashford told BT Sport. "We managed to score three goals but it could have been a lot more".
