Marouane Fellaini opened the scoring with 10 minutes left to play in the first half, and compatriot Romelu Lukaku added to the advantage after the break. Marcus Rashford also got on the scoresheet for United.
Here's a look at the team sheet, via Simon Peach of the Press Association:
Anthony Martial started the match with a dreadful miss from close range, as the Frenchman couldn't convert after a tricky corner kick. United dominated and mustered several good chances, but Henrikh Mkhitaryan's header missed the target and Lukaku aimed a shot at the goalkeeper.
The hosts suffered an early setback when Pogba appeared to pull his hamstring, with the Frenchman dropping to the pitch immediately. He was unable to continue, and Samuel Luckhurst of the Manchester Evening News felt for the midfielder:
But United's dominance continued, with Tomas Vaclik somehow denying Mkhitaryan. Luca Zuffi missed a rare chance for the visitors, and shortly after, substitute Fellaini gave the hosts a deserved lead off a great cross from Ashley Young.
Tom Coast of Sport Witness couldn't help himself:
Mohamed Elyounoussi was left wide open to power a header straight at David De Gea, but Basel couldn't threaten any further to end the half.
The Swiss side started the second half well, but the first real chance of the period resulted in another goal for United, with Lukaku heading home after another great delivery, this time from Daley Blind.
Per WhoScored.com, Lukaku has been in sensational form of late:
Set pieces were a clear weakness of Basel, and Lukaku went close yet again after 62 minutes, with Vaclik making another great save. On the other side of the pitch, main danger man Elyounoussi threatened again, but De Gea was determined to preserve his clean sheet.
Rashford missed a golden opportunity to add a third goal but redeemed himself in the final minutes with a poacher's goal.
Both teams will continue Champions League group play Sept. 27 when United travel to CSKA Moscow and Basel host Benfica.