Juan Mata's clinical penalty on the brink of half-time, awarded for a foul on Brandon Williams, might have been enough to see off the Hatters. However, Ole Gunnar Solskjaer made sure his side progressed by bringing on Bruno Fernandes, Mason Greenwood and Marcus Rashford as second-half substitutes and the trio combined well as the latter lashed in a late second goal.
Greenwood then made it 3-0 with a trademark strike in injury time, to give the scoreline some gloss, but in between United's first and second goals, Luton fashioned one notable opportunity to equalise.
The Hatters were thwarted twice in that same attack, by an excellent save from Dean Henderson, making his senior Reds debut, and then Eric Bailly's goal-line block as the ball remained in play.