Pierre-Emile Hojbjerg hooked in a 62nd-minute corner for his first Saints goal and Manolo Gabbiadini then had a 73rd-minute penalty brilliantly saved by Christian Walton before Cedric Soares added a second in stoppage time.
“I was delighted, I have to say," said new Saints boss Mark Hughes of the performance.
“It was a difficult fixture for us against a Wigan side whose manager and staff deserve huge credit for the way they set up and their philosophy of how they want to play.
“This year they've gone up against other top Premier League clubs and overcome them, so we were the next in line, apparently, but we weren't prepared to play that game.
“We had to match their intensity and endeavour – that's what lower league teams will always have in abundance.
“If you don't match that, sometimes you can come unstuck, but as a consequence of matching their endeavour, we were able to show the level of quality we have above them.
“That's eventually what's taken the game away from them, so I'm delighted, because it wasn't easy for us leading up to the game with a lot of change at the club.
“The players could've found that difficult to deal with, but they've been first class since I walked through the door. It's a good start for us, but that's all it is, so we have to build on this now."