Both teams started the game at Old Trafford brightly with United’s only shot on target coming in the first 45 minutes from Marcus Rashford.
After a goalless first-half, Presnel Kimpembe converted Angel Di Maria's corner kick to give the visitors the lead in the 53rd minute.
Seven minutes later, Di Maria played Kylian Mbappe through on goal to double the lead and the France star made no mistake in putting the ball past David De Gea, after beating Bailly and Lindelof with pace.
Ole Gunnar Solskjaer's side now face an uphill task to overturn the deficit in Paris in a fortnight and the Ivorian star who was on parade for the entire 90 minutes has described the result as a disappointment with their hopes of progressing to the quarter-finals dealt a huge blow.
"It's difficult, it's a big disappointment. We were off to a good start," Bailly said after the match.
"In the first half, we were fine. We conceded a goal from a set piece and took a blow to our morale. Then we conceded a second goal.
"Now we're going to forget about this game. There are more matches to come and think about in the future.
United went into the game with an unblemished record of 10 wins and a draw since the appointment of their interim boss Ole Gunnar Solskjaer and the 24-year-old claimed that they were not overconfident.
“No, we played on our strengths. We played on the counter-attack,” he added.
"The first half we were good, we defended well. On a mistake, we conceded the first goal.
"After that, the team tried to give its best. Unfortunately, the second goal came next, so it's a shame."