Marouane Fellaini gave the home side the lead in the closing stages of the first half before further goals from Chris Smalling, Henrikh Mkhitaryan and the returning Bastian Schweinsteiger saw the holders safely into the last 16.
United boss Jose Mourinho opted to hand rare starts to the likes of Schweinsteiger and Luke Shaw as he made nine changes to the side beaten by Hull City in the second leg of the EFL Cup semi-final on Thursday.
As was the case at the KCOM Stadium, though, United made a slow start to the match and it was Wigan who were the first to come close when Callum Connolly's sweetly-struck shot stung the palms of Sergio Romero in the United goal.
It wasn't until midway through the half that United finally threatened a breakthrough when a lofted ball into the box was only cleared as far as Juan Mata, who volleyed his effort narrowly over from the edge of the area.
United, bidding to become just the sixth team to retain the FA Cup this season, should have taken the lead shortly after the half-hour mark when Anthony Martial and Timothy Fosu-Mensah combined to set up Mkhitaryan on the counter-attack, but the Armenian somehow put the ball wide with the goal gaping.
Wigan continued to hold their own, though, and almost broke the deadlock themselves with five minutes remaining of the first half when Sam Morsy teed up Michael Jacobs, only for the midfielder to fluff his lines and miss the ball when trying to pull the trigger.
Just as it looked as though the visitors would go into the break all square United took the lead, with Fellaini outmuscling Connolly at the back post to nod home Schweinsteiger's cross.
The home side began the second half brighter and pushed for a second goal to give themselves a cushion, but Fosu-Mensah skewed one effort wide when well placed before Schweinsteiger saw a shot blocked having broken into the box.
Wigan could have levelled things up shortly afterwards when Romero pushed a low cross straight into the path of David Perkins, but the United keeper redeemed himself by denying the follow-up effort.
Once again, United punished the miss with a second goal to take a big step towards the last 16 as Smalling - one of only two players to keep his place from Thursday's defeat at Hull - towered above Stephen Warnock at the back post to convert Martial's cross.
Wigan, who have scored a league-low 24 goals in the Championship this season, showed few signs of overturning the two-goal deficit, with a weak Connolly header the closest they were able to come before United killed the game off once and for all with their third goal.
The visitors' attempts to claw their way back into the match left them susceptible to the counter-attack, and a devastating break from Mkhitaryan and Martial ended with the former converting from close range 16 minutes from time.
Wigan debutant Marcus Browne almost made an immediate impact off the bench when Smalling was needed to block a shot with his first touch, but it was United who seemed in the mood for more goals and Burn almost gave them a helping hand when he turned Martial's knockdown narrowly over his own crossbar.
The biggest cheer of the afternoon was reserved for Schweinsteiger, though, and the German marked his first United start in over a year by capping off the scoring with an acrobatic bicycle kick from close range after Ander Herrera had nodded Rooney's corner into a dangerous area.
United had the ball in the back of the net for a fifth time in the closing stages through Martial, but the whistle had already gone for a high foot and the hosts ultimately settled for a second consecutive 4-0 win in the defence of their FA Cup crown.
The result means that United have now won all nine of their home matches against Wigan, scoring 32 goals in the process while conceding just one.