Jose Mourinho's side who won 2-1 on aggregate, dominated the match with Zlatan Ibrahimovic coming close twice in the first half.
The win though, came at a price as United who are already missing Wayne Rooney and Antony Martial through injury saw Paul Pogba subbed with a hamstring injury.
United, who have never won the title, will know their last eight opponents this afternoon during the draw in Nyon.
Meanwhile, England Manager Gareth Southgate has recalled Sunderland striker Jermaine Defoe to the side, ahead of their friendly against Germany and world cup qualifier against Lithuania, this month.
The 35-year-old returns to the three lions squad after over three year absence.
Manchester United striker Marcus Rashford and defender Luke Shaw are among the players named in the squad.
Captain Wayne Rooney, Tottenham striker Harry Kane, alongside Liverpool pair of Jordan Henderson and Daniel Sturridge all miss out through injuries.
Another notable omissions is Arsenal's Theo Walcott.