On the back of a first leg 2-0 defeat at Old Trafford, the Red Devils moved swiftly to turnaround the deficit with an early goal from Romelu Lukaku.
The Parisians levelled through Juan Bernat before Lukaku's second and Marcus Rashford’s late-minute penalty saw Ole Gunnar Solskjaer’s men move into the quarter-finals of the competition on away goals after a 3-3 aggregate draw.
The Cote d’Ivoire international who missed the Red Devils’ last outing to Southampton featured for only 36 minutes in the encounter after picking an injury.
Impressed with the incredible feat by his side, the defender has taken to the social media to show his delight.
“Incredible win, feels great to be in the next round. Proud to be part of this family,” Bailly tweeted.
The former Villarreal player has made 17 appearances for Manchester United this season in all competitions.
He will hope to be involved when they visit the Emirates Stadium to tackle Arsenal on Sunday.