The only worrying moment for the hosts was the early withdrawal of captain Paul Pogba due to injury although Jose Mourinho was able to turn that negative into a positive when the change brought the Red Devils' first goal with substitute Marouane Fellaini opening the scoring ten minutes before the break, heading home Ashley Young's perfect cross.
The lead was doubled on 53 minutes when Romelu Lukaku netted his sixth in six games, heading Daley Blind's drilled cross in after the hosts took advantage of a Basel side that was slow to react to a quickly taken short corner.
Another Mourinho change made the final mark of the game when second-half substitute Marcus Rashford somehow found the net after mis-hitting his shot into the turf with the ball bouncing high into the net.
Basel rarely looked like they would take anything from this game and sat back in numbers for large periods of the match although they did enjoy a couple of good efforts on goal, forcing a fine save out of David De Gea on 64 minutes when Mohamed Elyounoussi shot was tipped over.
However it was the hosts' night and the Red Devils did have more opportunities to add to the scoreline, particularly in the first half with Henrikh Mkhitaryan missing two great chances, including hitting the post from close range.