The Blades started with Chris Basham in midfield and Conor Sammon in attack, Matt Done on the bench.
For the first 45 minutes United struggle to create many clear-cut chances, Billy Sharp and Jose Baxter going close with long-range efforts.
At half-time, Nigel Adkins brought on Che Adams for Sammon, and Sharp had a close-range effort well saved by Jussi Jaaskelainen.
Wigan forced George Long to tip over from Conor McAleny, but it was never going to be a repeat of the 3-3 game between the two sides in Lancashire last month.
Two goals three minutes, though, turned the match.
Basham was punished for a foul in the box, and Will Grigg converted from the penalty spot on 52 minutes.
On 55 minutes, it was 2-0, after slick passing cut open United and McAleny drilled home beyond Long.
Jay McEveley dragged his effort wide following a surging run down the left flank, but the Blades could not conjure up a goal.
And it needed Long to save a second Wigan penalty to prevent the scoreline reaching 3-0.
Adkins said: “I thought it was a very close game, both goalkeepers had very little to do.
“Wigan are a very good side and we go in 0-0 at half-time.
“We make a technical change, bring Che Adams on, and he looked bright, but the turning point was the penalty.
“It was a poor decision from ourselves with the challenge, there was no need to make it, there were three or four players around him.
“The referee had no option to give the penalty.
“Following on fron that, our throw-in, we cheaply give the ball away and the lad scores a good goal. It changed the game.
“We had a few chances, but we didn’t get the victory and that was what we were all after.”