Young Boys dominated the early stages, the pace of Kevin Mbabu and Roger Assale caused the United defence all sorts of problems.
Meanwhile, the Red Devils looked lacklustre and disjointed in attack, with only full-backs Luke Shaw and Diogo Dalot offering United any attacking threat.
However, this all changed when out of nothing, Paul Pogba created a moment of magic. From just outside the box, Man Utd's captain for the night drilled a left footed shot into the top left corner.
In the 42nd minute, the match turned again. Referee Deniz Aytekin adjudged Young Boys' full-back Mbabu to have handled the ball in the box, and a penalty was given. Pogba, with his outrageously slow run-up, coolly blasted the penalty into the top right corner.
In the second-half, Anthony Martial scored his first goal for the club since January, when he slotted home after a wonderful Paul Pogba pass.
What could have been a tricky visit to Bern for Mourinho's side, ended up being a routine win.
Key Talking Point
Much of the pre-match build up was focused on how the three-time European champions would cope with playing on Young Boys' plastic pitch.
After a difficult start to the match which saw many of the Manchester United players slip over at crucial moments, Jose Mourinho's side eventually adjusted to the different speed of play an artificial pitch brings.
In the end, the pitch caused United few problems, and the fans and manager alike will be pleased that they came away with no new injury concerns
Starting XI: De Gea (8); Dalot (7), Smalling (7), Lindelöf (6), Shaw (7); Fred (6), Matic (7), Pogba (9); Rashford (7), Lukaku (5), Martial (6).
Substitutes: Mata (6), Fellaini (7), Perriera (6).
Star Man - Paul Pogba
The 25-year-old midfielder put in a performance which any of the great Man Utd's captains of the past would have been proud of.
He dominated the midfielder, perfectly balancing attack and defence. His first goal transformed the match, scoring at a time when the Premier League side were seemingly on the ropes. The goal not only gave United the belief that they could win the game, but also silenced a bouncing Stade de Suisse which was right behind the home team.
Without Pogba, Manchester United could easily have drawn or even lost this match.
Paul Pogba, take a bow 👏 such a classy player. What a finish. Captain fantastic!— Liam Canning (@LiamPaulCanning) September 19, 2018
Worst Player - Romelu Lukaku
By no means a terrible performance for the Belgian striker, he just looked a little off the pace and was not always making the runs which his fellow United team-mates desired.
Other players who struggled were summer signing Fred, and Anthony Martial also missed a string of chances prior to his goal.
Starting XI: Von Ballomos (7); Mbabu (8), Ali Camara (6), von Bergen (6), Benito (6); Fassnacht (6), Sow (7), Sanogo (7), Sulejmani (7); Hoarau (7), Assale (8).
Substitutes: Aebischer (6), Ngamaleu (6), Nsame (6).
Star Man - Kevin Mbabu
How Newcastle fans will be ruing the day they sold Kevin Mbabu. The 23-year-old Swiss full-back was electric on the right side of the pitch and offered his side a real threat in attack.
He was desperately unlucky to give away the penalty, considering the speed at which the ball was travelling towards him and the position of his hand.
A career at one of the top clubs could beckon for the young full-back
Worst Player - Christian Fassnacht
No stand-out worst player for Young Boys as everyone of their players played with great heart and perseverance. Unfortunately, to single out one player individually, Christian Fassnacht was at times wasteful in possession.
United's next match is a tricky one, at home to Premier League new boys Wolverhampton Wanderers. Before their next match in the Champions League against Valencia, Man Utd also have to contend with a Carabao Cup match against Derby County and a visit to West Ham.
With Juventus' Cristiano Ronaldo possibly suspended for the next three Champions League matches, Manchester United can consider themselves serious contenders for topping the group come December