With its progress to the next round all but secured after a thumping 4-0 first-leg win in Turin last week, Ole Gunnar Solskjaer opted to start with Marcus Rashford, Harry Maguire and Luke Shaw on the substitutes' bench, while Dean Henderson replaced David de Gea in goal.
Mikel Oyarzabal should have taken advantage of a sluggish start from United, but his early penalty flew well over, while Bruno Fernandes and Daniel James went close for the host before the break.
Substitute Axel Tuanzebe saw an effort ruled out during an insipid second half, though it mattered little in the end as United booked their place in Friday's last-16 draw with the minimum of fuss.
La Real were given a golden opportunity to take a 13th-minute lead when James clumsily brought down Andoni Gorosabel in the penalty area, but Oyarzabal blazed the resulting spot-kick over.
Only a superb touch from Victor Lindelof prevented Alexander Isak tapping home at the back post soon after, while Anthony Martial was denied by Alex Remiro at the other end as United belatedly woke from their slumber.
Fernandes then whipped a fine effort against the crossbar from 16 yards before Remiro pawed away James' header shortly before half-time.
Rashford replaced Fernandes at the break and flashed a 30-yard free-kick past Remiro's left-hand post soon after, while Modibo Sagnan headed against the crossbar for the LaLiga side.
Tuanzebe thought he had scored his first United goal shortly after the hour mark, but his powerful header was ruled out for a foul by Lindelof following a pitchside review by referee Lawrence Visser.
Shola Shoretire became United's youngest ever player in European competition at the age of 17 years and 23 days when introduced with 14 minutes remaining as the Red Devils stretched their unbeaten run at home in the Europa League to 15 games.