The Stoke striker drove a powerful shot past Wigan keeper John Filan after good work by Clive Clarke down the left.
Jimmy Bullard missed Wigan's best chance, slicing his shot after beating two defenders to make space.
Noel-Williams missed a chance to seal the points 10 minutes from time, his tame effort gave Filan an easy save.
Stoke boss Tony Pulis on Gerry Taggart:
"Gerry's been here just over 18 months and he's been fantastic. He can't run, he's an old-fashioned player.
"Because he's like that you look at him and think that he's going to struggle against quick strikers.
"But he's a warrior and he enjoys the battle. He doesn't enjoy the pretend stuff in training - he wants to be out there in the middle."
Wigan: Filan, Eaden, Thome, Jackson, Baines (Graham 82), Teale (Johansson 75), Bullard, Mahon, McCulloch, Roberts, Ellington.
Subs Not Used: Walsh, Breckin, Jarrett.
Booked: Thome, Teale.
Stoke: Simonsen, Buxton, Taggart, Hill, Hall, Asaba, Eustace (Henry 47), Brammer, Clive Clarke, Noel-Williams, Greenacre.
Subs Not Used: de Goey, Neal, Gudjonsson, Gudmunsson.
Booked: Taggart, Hall, Asaba, Buxton, Simonsen.
Goals: Noel-Williams 39.
Ref: M Clattenburg (Co Durham).