A winner from Marcus Rashford, deep into extra-time, finally saw off Anderlecht to cap a thrilling night at Old Trafford and send United into the Europa League semi-finals.
They took the lead on 10 minutes when excellent work from Paul Pogba and Marcus Rashford created a chance which Henrikh Mkhitaryan powered home, and looked likely to add to their advantage in the following few minutes.
Marcus Rashford had an assist and a goal, while Fellaini assisted the late winner.