Following a shaky start, Diogo Dalot opened the scoring for the visitors midway through the first half with a superb curling strike, before captain Bruno Fernandes converted from the penalty spot on the 74th-minute mark to seal a dominant win for the Red Devils.
Erik ten Hag's side were wasteful in the final third, but they ultimately got the job done, despite a dogged display from Shaun Maloney's side, to secure their place in the fourth round and set up an intriguing tie away against either League Two side Newport County or non-league outfit Eastleigh later this month.
In front of a fired-up DW Stadium, Wigan almost made the perfect start to the contest inside the first three minutes when Sean Clare and Martial Godo combined during a great break down the right, before the latter delivered an inviting cross to the back post for Thelo Aasgaard, whose low-driven shot was saved by the outstretched Andre Onana.
United responded well but were initially thwarted by a disciplined Wigan backline and goalkeeper Sam Tickle, who was forced to make a great diving save low down to his left to deny Marcus Rashford.
An intricate passing sequence from the visitors on the edge of Wigan's box resulted in Scott McTominay side-footing an effort on goal, but the Scotsman's strike bobbled wide of the far post.
Dalot made no mistake in front of goal just a few minutes later, though, as he opened the scoring in the 22nd minute with a beautifully-shaped strike into the bottom corner from outside the penalty area to help settle Man United's nerves.
United deserved to be in front and they almost scored a second just two minutes later after a shot from Rashford was initially fumbled by Tickle onto the post before falling into the grateful hands of the Wigan goalkeeper.
The Red Devils continued to dominate in the final third and had a total of 17 shots in the first 45 minutes, but they ultimately lacked a clinical edge and wasted a number of decent opportunities, with Rasmus Hojlund in particular left notably frustrated.
After Tickle denied Hojlund with an outstretched left leg, the Danish striker clipped the top of the crossbar with a powerful diving header from close range.
Hojlund then somehow failed to steer a side-footed effort on target from just four yards out after Tickle parried a strike from Rashford, before McTominay directed a towering header wide from the edge of the six-yard area.
Alejandro Garnacho then came agonisingly close with a stunning left-footed strike from around 22 yards out, but his effort smacked the face of the crossbar and Man United were forced to enter half time only one goal ahead.
Ten Hag's side picked up from where they left off in the second half, dominating proceedings as they looked to find a way through Wigan, but the hosts' backline stood firm to block a curling effort from Fernandes following a neat one-two with Hojlund.
Out of nowhere, Aasgaard almost capitalised on a lapse of concentration in the Red Devils defence, but the Latics attacker was denied by Onana, before and inviting cross from Godo on the left flank sailed over his teammate and out for a goal kick.
Kobbie Mainoo came close to scoring his first senior goal for Man United just after the hour mark when he fired a low-driven shot towards the bottom corner, but Tickle produced a fine diving save to his right, before Liam Morrison capitalised on a hesitant McTominay to deflect the midfielder's shot over the crossbar.
Man United were then awarded a somewhat soft penalty in the 74th minute when Fernandes chopped back and fell to the floor after feeling contact on his boot from Wigan's Liam Shaw.
With no VAR in the FA Cup, the on-field decision from Anthony Taylor stood, and Fernandes stepped up to convert his 28th penalty out of 32 for the Red Devils, sending Tickle the wrong way as he coolly slotted his effort into the bottom-left corner.
Aasgaard had Onana scrambling in the closing stages, but the Cameroonian had it covered and watched the dragged strike roll wide, before United saw out the final few minutes with ease to the delight of the 7,506 travelling Red Devils supporters.
Man United will now turn their attention to Sunday's Premier League contest at home against Tottenham Hotspur, while Wigan travel to Northampton Town for a League One fixture on Saturday.