Manuel Lanzini's early strike was all that separated the two sides in a tie where Ole Gunnar Solskjaer decided to not include Cristiano Ronaldo in the squad.
Both sides had their fair share of chances with Mark Noble, who's penalty heartache stopped West Ham from claiming a point at the weekend, missing a guilt-edge chance.
But Noble's miss proved academic as David Moyes' side held on for the win.
Man United are the highest-profile exit from the competition at this stage but Chelsea and Tottenham came mighty close to crashing out as they needed penalties to beat Aston Villa and Wolves respectively.
Elsewhere, Arsenal swept aside League One AFC Wimbledon 3-0, while Leicester won 2-0 at Millwall and Brighton beat Swansea by the same scoreline.
This is a breaking news story. More updates will follow shortly.
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