The Red Devils won 2-0 on the night to seal a 4-0 victory on aggregate against Granada.
Edinson Cavani continued his rich vein of form as he opened the scoring in the sixth minute, and Juan Mata’s deflected header doubled their advantage late on.
Arsenal stunned Slavia Prague with a lightning start in the Czech capital to blow away their opponents and comfortably progress in what was a tricky-looking assignment.
The Gunners knew they needed to score after drawing the first leg 1-1 at the Emirates and were in front after 18 minutes through Nicolas Pepe.
Alexandre Lacazette made it 2-0 from the penalty spot just three minutes later and it was 3-0 shortly afterwards as Bukayo Saka got his name on the scoresheet.
Lacazette wrapped up the scoring in the second half to give Arsenal a 5-1 win on aggregate.
Roma progressed against Ajax after drawing 1-1 on the night in a game which saw ex-Manchester City striker Edin Dzeko cancel out Brian Brobbey’s opener to make the aggregate score 3-2.
Villarreal complete the last-four line-up after beating Dinamo Zagreb.
Strikes from former Barcelona striker Paco Alcacer and Gerard were enough to seal a 2-1 win on the night and a 3-1 triumph on aggregate for the Yellow Submarine. Mislav Orsic netted Dinamo’s consolation.
The first legs of the semi-finals will be played on Thursday April 29, with the second legs taking place a week later.