Tom Huddlestone's controversial first-half penalty and Oumar Niasse's late strike earned victory for Marco Silva's side on the night, but Paul Pogba's 66th-minute goal ensured United progressed 3-2 on aggregate.
Ultimately, Marouane Fellaini's late goal in United's 2-0 victory at Old Trafford a fortnight ago proved the defining moment in the tie as Hull fell agonisingly short of an unlikely comeback, despite ending United's 17-game unbeaten run.
