Juan Mata scored the only goal of the contest at Old Trafford to send Jose Mourinho's men through to the next knockout phase where they may come up against former player Memphis Depay's Lyon, who defeated AS Roma 5-4 on aggregate despite last night's 2-1 defeat in the Italian capital.
It could be an interesting tie if United and Lyon are drawn against each other but the fact Depay is cup-tied takes a little bit of spice out of the potential encounter.
Belgian side Anderlecht accounted for Cyprus' APOEL Nicosia 1-0 at home to win 2-0 on aggregate, joining Jupiler League rivals Genk in the final eight after they overcame domestic opponents Gent 6-3 on aggregate after a 1-1 second leg draw.
Germany's Schalke were involved in the most dramatic match of the Round of 16 second legs by overcoming Bundesliga rivals Borussia Monchengladbach on away goals.
Last week's 1-1 draw in Gelsenkirchen was succeeded by a 2-2 outcome in Monchengladbach after the home side had taken a two-goal lead through Chelsea's Andreas Christensen and a stunner from Mahmoud Dahoud.
Dutch powerhouse Ajax successfully navigated their way through, coming from 2-1 down against Denmark's FC Copenhagen, to win the second leg 2-0 at home through goals from Chelsea loanee Bertrand Traore and Danish striker Kasper Dolberg.
Spanish side Celta Vigo are struggling domestically in 11th position but placed their La Liga woes behind them to account for Russian outfit Krasnodar with a 4-2 aggregate win following a 2-0 home triumph courtesy of goals from Hugo Mallo and Iago Aspas.
And finally, Turkish giants Besiktas hammered Olympiakos 4-1 despite being reduced to ten men late in the first when opening goalscorer Vincent Aboubakar had received a straight red card from Michael Oliver for an off-the-ball headbutt.
The Istanbul side won 5-2 on aggregate.
*The draw for the 2016/17 UEFA Europa League quarter-finals will be made in Lyon, Switzerland at 12:00pm CET on Friday.
Europa League final eight