Ahead of Tuesday’s clash at Old Trafford, the Reds knew a place in the next round would be sealed with a win against the Swiss side, as long as Juventus beat Valencia in Turin.
While Young Boys made it tough throughout, that scenario is exactly how things panned out on the night thanks to Fellaini's injury-time clincher and Juve's 1-0 victory via a second-half Mario Mandzukic strike.
Along with Juventus, United were one of six sides who ensured qualification for the next round on Tuesday.
In Group E, Ajax kicked off the fifth round of group games by beating AEK Athens 2-0 in Greece, meaning they will definitely finish in the top two spots.