The 19-year-old replaced Timothy Fosu-Mensah at Old Trafford with the hosts leading 2-0 thanks to goals from Marouane Fellaini and Chris Smalling.
Further goals from Henrikh Mkhitaryan and Bastian Schweinsteiger added gloss to the scoreline as the holders eased into the fifth round of the competition.
Tuanzebe was part of the squad that travelled to Hull City on Thursday for the second leg of their EFL Cup semi-final but was not used against the Tigers.
A handshake and a hug for Tuanzebe from Mourinho before he comes on #MUFC— Kris Voakes (@krisvoakes) January 29, 2017
Wigan boss Warren Joyce will know all about Tuanzebe after helping bring the youngster through at United, during his time as reserve team boss.
Joyce spent eight years at the club before leaving in November, replacing Gary Caldwell in charge of the Latics.
Mourinho also handed Joel Pereira a first-team debut, the goalkeeper replacing Sergio Romero for the final 10 minutes of the game.