United had already secured top spot in their group and thus multiple key players, including Cristiano Ronaldo and Bruno Fernandes, weren't included in the squad.
Mason Greenwood gave the home side the lead with a wonderful finish after just nine minutes.
Young Boys battled back and Fabien Rieder's superb curling effort meant the two sides went into the break level.
There were no further goals in the second half as the points were shared.
Eric Bailly was chosen to start by Ralf Rangnick on the evening.
The Ivorian isn't a guaranteed starter at United but he always provides comedy when he does take to the field.
And he was at it again on Wednesday evening as he produced two amusing moments in the first half.
Bailly produced a lovely slide tackle to dispossess an opponent. Instead of just standing up Bailly decided to a spin before getting to his feet.
If that wasn't enough, Bailly did it once again later on in the half.
The defender produced a fine clearance inside his own six-yard box and then spun a full 360 degrees before getting to his feet again.
Many football fans enjoyed Bailly's actions and you can view some reaction below.
Never change, Eric.
The Football Terrace: Ralf Rangnick's 4-2-2-2 Revolution!
United finished top of Group F. Their possible opponents in the last 16 include Paris Saint-Germain, Atletico Madrid and Inter Milan.