The only goal came after 54 seconds but, for much of the game, United were a shadow of the team which beat Chelsea so convincingly on Sunday.
Wigan, who have now lost all eight meetings against Sir Alex Ferguson's side in the Premier League and Carling Cup, were unlucky not to take a point from this latest encounter.
But the result was all that counted in the end with victory moving United two points behind leaders Liverpool.
United will end the week on top of the table if they win at Bolton on Saturday, although they will have to play far better at the Reebok.
Wayne Rooney's early goal was his sixth against Wigan in the last four seasons.
The Latics were caught cold when Dimitar Berbatov's raking pass found Cristiano Ronaldo on the right.
The FIFA World Player of the Year beat Maynor Figueroa on the edge of the box before supplying the low cross which Rooney tapped home from close range in the centre of goal.
Six minutes later though Rooney was replaced by Carlos Tevez after signalling to the United bench that he had a hamstring problem which will keep him sidelined for three weeks.
Wigan goalkeeper Chris Kirkland had to race out of his box midway through the first half to head clear from Ronaldo and United should have added to their tally in the 25th minute.
John O'Shea's innocuous header out of defence saw Tevez steal a march on a lethargic Wigan defence when he ran clear just inside the Latics half.
The Argentinian rounded Kirkland but took the ball too far and, when his shot came in, it was easily blocked by Titus Bramble on the left by-line.
Wigan pressed forward, although they failed to capitalise on slack United defending numerous times.
United went close to scoring a second goal in the 38th minute. Nani's cross from the right side of the Wigan penalty area was missed by both Ronaldo and Tevez, and when Paul Scholes fired in an shot from 12 yards, it was blocked by Mario Melchiot.
Wigan forced the pace after the interval and it took a fine save by United goalkeeper Edwin van der Sar after 67 minutes to keep out a powerful 20-yard shot from Figueroa but in the end Rooney's early goal proved to be decisive.