It was Hughes' first game in charge of the Saints and for long periods in the first half it looked as if it could end in embarrassment as League One Wigan dominated.
A much-improved display after the break saw Southampton score twice, with Pierre-Emile Hojbjerg and Cedric Soares both netting their first goals for the club. Manolo Gabbiadini also had a penalty saved but it mattered not as Hughes' team won to set up a Wembley meeting with Chelsea.
“I was delighted, I have to say,” Hughes told Southampton's official website. “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."
Wigan were aiming to reach their third FA Cup semi final in six seasons and had already produced a memorable run to reach this stage, knocking out Premier League clubs Bournemouth, West Ham and Manchester City.
“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," said Hughes.
“We had to match their intensity and endeavour – that’s what lower league teams will always have in abundance."
Southampton's attention will return to the Premier League after the international break, with a crucial trip to West Ham first up. Saints dropped into the relegation zone on Saturday as a result of Crystal Palace's win at Huddersfield.