Donny van De Beek and Dean Henderson were handed their first starts for United whilst Aaron Wan-Bissaka, Eric Bailly, Fred, Juan Mata and Odion Ighalo were amongst others featured in United’s line-up.
The Red Devils asked the first questions following the earlier exchanges with Mata drawing Luton goalkeeper James Shea to a near post save before Harry Maguire strayed wide from range.
Shea was given further duties later on when a low ball from Jesse Lingard and dummy from van De Beek found Mata, who watched his first-time strike beaten away.
Following a lukewarm spell, United took the lead on 44 minutes after Mata sent Shea the wrong way from the penalty spot as Brandon Williams went down in the area.
Luton pinned the Red Devils in their own half following the start of the second half, with Williams, Wan-Bissaka and Maguire forced in a compact zone while Lingard fired over at the other end.
Ole Gunner Solskjaer introduced three substitutions in a bid to kill off the contest following the final 12 minutes in Bruno Fernandes, Marcus Rashford and Mason Greenwod.
Luton threatened to draw level two minutes later after Tom Lockyer had Henderson scrambling on the goal-line following a back-post header and smothered the follow-up too.
The Red Devils however put the result beyond doubt on 88 minutes after Greenwood played in Rashford, who made no mistake from close-range for his first goal of the season.
United put the icing on the cake in stoppage time when Greenwood broke free on the right to curl beyond Shea for a comfortable victory in the end.