It took a while for United to open the scoring but when they did it was a comfortable night for the team. Marouane Fellaini was the man to open the scoring with Romelu Lukaku and Marcus Rashford scoring the other goals to give United three important points.
United, therefore, end matchday one on top of the table and will go on to face CSKA Moscow in a couple of weeks time, while Basel play Benfica in their second game.
Mourinho made quite a few changes to his starting lineup
José Mourinho made six changes to his team for the game with Ashley Young, Anthony Martial, Victor Lindelof, Chris Smalling, Juan Mata and Daley Blind coming into the starting XI after the weekend's draw against Stoke City.
Mkhitaryan missed two glorious chances to give United the lead as Pogba came off injured
The game itself went as expected early on with the home side having plenty of the ball with the visitors happy to sit back and counter whenever they could.
It took a while for the first big chance of the game to come but when it did it fell the way of Henrikh Mkhitaryan after a brilliant passing move ended with Mata crossing the ball to Mkhitaryan, who was unmarked in the box but somehow he put his header over the bar when he should have scored.
Moments later, though, United suffered a big blow in the game when Paul Pogba had to be substituted with a suspected hamstring injury which will give Mourinho a further headache ahead of a busy period of matches.
It didn't stop United going forward though as once again Mkhitaryan missed a glorious chance to give the team the lead. Lukaku played a great cross into the box but Mkhitaryan saw his first shot come back off the post before seeing the his follow up effort saved.
Them missed chances almost proved costly as the visitors went down the other end and almost scored with their only chance of the game. The ball fell to Luca Zuffi in the box but he put his shot well wide of the goal when he should have done much better.
Fellaini gave United a much deserved lead before half-time
All of United's pressure though did finally pay off 10 minutes before the break when a great cross into the box from Young found Fellaini in the box and he powered his header home to give the hosts the lead at half-time.
Lukaku and Rashford added goals in the second half to give United the pefect start
It didn't take Mourinho's men long to make it two in the second half as eight minutes in, a great cross from Daley Blind was headed into the back of the net by Lukaku, who was making his first ever appearance in the Champions League.
Lukaku could have had a second goal a few minutes later when he saw another header saved this time from a great free-kick from Mkhitaryan.
After that chance though United took their foot off the pedal and that allowed the visitors to gain confidence and they almost got one goal back when Mohammed Elyounoussi saw a good shot well saved by David de Gea.
That though was the only real scare that United had in the second half and they managed to round the night off with a third goal. A brilliant run into the box from Fellaini, who put in a great cross, found Rashford, who scored on his Champions League debut to give United a winning start to their campaign.