Diogo Dalot curled home midway through the first half as United dominated most of the play, with Rasmus Hojlund, Scott McTominay and Marcus Rashford all going close and Alejandro Garnacho striking the crossbar.
The home side had goalkeeper Sam Tickle to thank for keeping them in the game for large periods, but the Latics' no.1 could not prevent Bruno Fernandes from doubling the scoreline with a penalty he'd won himself, 15 minutes from time.
Erik ten Hag's men, who were cheered on by 7,500 travelling Reds on a freezing Monday evening, can look ahead to another visit to a side in a lower English league at the end of the month, with the Eastleigh v Newport replay to be settled first on Tuesday 16 January.