Rasmus Hojlund's early double was enough to give Manchester United a fifth straight victory in all competitions, although Luton Town pushed us all the way in our first league visit to Kenilworth Road in 32 years.
Hojlund capitalised on a defensive error to open the scoring after just 37 seconds and then chested home to leave us seemingly in cruise control.
Carlton Morris's header hoisted the Hatters right back into the encounter, however, and the hosts closed out the first half impressively.
United could and perhaps should have scored a third and decisive goal after the break but were left hanging on a little at the end, as Luton besieged our goal and struck the crossbar in the dying moments through Ross Barkley.