The hosts were the better team for long spells of the first half in what was their first appearance in the Champions League proper since its rebranding, but ultimately it was the quality of Paul Pogba which turned the match in United's favour.
The stand-in skipper scored twice in the space of nine first-half minutes to put United in control, and then added an assist to his haul by teeing up Anthony Martial for the winger's first goal since mid-January.
United ultimately cruised to the victory on the Swiss side's plastic pitch, leaving themselves top of Group H after the first game, level on points with Juventus courtesy of their victory over Valencia.
Jose Mourinho handed a debut to Diogo Dalot in addition to recalls for Luke Shaw, Martial, Fred and Marcus Rashford, but the visitors still struggled to get going in the first half as Young Boys carried a persistent threat on the counter-attack.
The Swiss champions - already eight points clear at the top of their domestic league - signalled their intent to break quickly early on and they could have taken the lead after only eight minutes when former Newcastle United defender Kevin Mbabu's cross was glanced narrowly wide by Guillaume Hoarau.
United's own sights of goal were few and far between, with Romelu Lukaku hitting one effort into the side-netting before Rashford clipped the outside of the post with a clever flick from Shaw's low cross.
It was Young Boys who looked the most like breaking the deadlock for much of the opening 45 minutes, though, with United being forced to repel a number of crosses into the box and David de Gea being called upon to tip Mohamed Camara's long-range effort over the crossbar.
Christian Fassnacht was one of the home side's brightest attackers and broke into the box before seeing his shot blocked and fall into the path of Djibril Sow, who dragged his long-range rebound wide of the target.
Fassnacht came close again shortly afterwards when his rising drive from just outside the area was tipped over by De Gea, but it was the lack of a telling piece of quality in the final third which was costing the hosts, and that came back to haunt them with 10 minutes remaining in the first half.
There was certainly no quality lacking as Pogba picked up a loose ball just outside the area, shifting it smartly onto his left foot before picking out the top corner with a pinpoint finish which left David von Ballmoos with no chance.
The opener came against the run of play, but suddenly it was United who were piling on the pressure and Victor Lindelof caused panic in the area with a header from a corner before their second goal arrived with just one minute left of the first half - albeit in controversial circumstances.
Mbabu was unfortunate to be penalised for a handball inside the area after Shaw's cross struck him, but Pogba made no mistake with the subsequent spot kick as he picked out the top corner, despite the goalkeeper getting a touch to it.
It made for a harsh half-time scoreline against the home side, but United's two goals gave them control over the game upon the restart and Martial had a decent chance to put the game to bed just three minutes after half time when he broke into the box but took too long over his finish.
There was still the occasional attacking foray from Young Boys as they searched for a route back into the match, with Roger Assale sending one inventive flick bobbling past the post before firing high and wide with a solo effort moments later.
United wrapped up the points shortly after the hour mark, though, as Pogba led the charge from midfield before playing in Martial, who again took his time over the finish but this time saw it deflect off the foot of Camara and past the helpless Von Ballmoos.
By that stage it was well and truly game over, although Young Boys should have at least grabbed a consolation when first substitute Michel Aebischer blazed over from inside the box and then Camara somehow clipped the outside of the post with a volley from point-blank range.
There was still time for United to almost add a fourth when Juan Mata reacted well to steer Shaw's driven low cross goalwards, but his instinctive effort zipped narrowly wide of the target and the visitors seemed content to rest on their three-goal advantage for the closing stages as they eased to victory, inflicting a first defeat of the season on Young Boys in the process.
United - who host Valencia in their next Champions League outing - will now turn their attention to Saturday's home match against Wolverhampton Wanderers, while Young Boys face a Swiss derby against Basel on Sunday afternoon.
YOUNG BOYS (4-4-2): Von Ballmoos; Mbabu, Camara, Von Bergen, Benito; Fassnacht (Ngamaleu 65'), Sow (Aebischer 59'), Sanogo, Sulejmani; Hoarau (Nsame 75'), Assale
MAN UTD (4-4-3): De Gea; Dalot, Smalling, Lindelof, Shaw; Fred (Fellaini 69'), Matic, Pogba (Pereira 75'); Rashford (Mata 69'), Lukaku, Martialbody check tags ::