United finished the job and progressed into the Europa League last 16 despite Eric Bailly's dismissal.
Leading 3-0 from last week's first leg, United grabbed the early away goal through Henrikh Mkhitaryan to put the tie beyond any lingering doubt.
The Armenian limped off shortly afterwards to make him a doubt for Sunday's EFL Cup final against Southampton at Wembley.
The goal came after a wonderfully intricate move on the quarter hour mark.
Juan Mata used Daley Blind's overlapping run as a decoy and instead drifted inside to guide a pinpoint cross to the back post.
Mkhitaryan did the rest and feathered the ball beyond the advancing Stephane Ruffier with a delicate touch.
Vincent Pajot almost put through his own net before Marcus Rashford replaced the hamstrung Mkhitaryan on 25 minutes.
Ashley Young fired across the face of goal, Bailly blocked well from Jordan Veretout and Loic Perrin headed straight at birthday boy Sergio Romero.
Rashford played in Zlatan to fire over the bar before a combination of Romero and Bailly thwarted Kevin Monnet-Pacquet when clean through.
The hosts now needed five to progress and never looked capable of even an equaliser, although Henri Saivet volleyed narrowly wide soon after the break.
Marouane Fellaini could have doubled the visitors lead when picked out by Blind, but the impressive Belgian could only find the side netting when well placed.
Ruffier saved well from Pogba but then came frustration for the Reds.
A second tackle by Bailly on Romain Hamouma in as many minutes saw him, perhaps harshly, booked on both occasions and the Ivorian was dismissed.
That means that Bailly will be suspended for the first leg of our last 16 tie, with United set to discover their opponents in Friday's draw.
Hamouma went close twice from distance, while the Pogba brothers both tried their luck at either end.
Florentin thumped a drive off target while Paul's header was hacked away to safety.
Rashford fired wide when one-on-one and substitute Bastian Schweinsteiger curled a shot narrowly over after nice build up play from Pogba.
Romero saved well to keep out Jorginho in the game's final action as United marched on and continued their four-pronged trophy tilt.
Overall team performance: 7.5/10
United Faithful man of the match: Juan Mata