Marcus Rashford's effort helped Ole Gunnar Solskjær’s men extend their unbeaten run to ten games.
Bailly who was handed his ninth league appearance and seventh start this season was impressive, helping the Red Devils to keep a clean sheet in the encounter.
And after claiming their seventh away win this term, the Cote d'Ivoire international took to the social media to applaud the Old Trafford outfit.
“A tough match, but we’re headed home with three more points,” Bailly posted on Instagram.
Bailly will hope to retain his spot when the Red Devils travel to the Craven Cottage to tackle Fulham on February 9.