Stewart's goal was surrounded by controversy as Wigan players and fans first of all thought the ball had gone out of play, but when the linesman waved play on and the cross came over an offside looking Stewart prodded the ball past John Filan.
The goal stunned the home fans in the biggest football crowd seen in the town since 1953, but Sunderland danced jigs of delight as the three points almost guarantees them promotion to the Premiership.
To be fair Sunderland looked the better side throughout with their passing crisper and more accurate than that of a Wigan side which failed to recover from Saturday's home defeat against West Ham.
Chances were few and far between, but Wigan might easily have gone in front even before Sunderland's opener when Gary Teale saw his shot parried by Thomas Myhre.
Jason Roberts and Nathan Ellington also went close as Sunderland defended what they had but they too might have added a second had Filan not made a smart save from Dean Whitehead.
Sunderland boss Mick McCarthy defended his side's decision to play on despite appeals for a throw in-and said: "The first rule of football is that you play to the whistle. Whether the ball went out or not I have no idea but it doesn't matter now.
"I won't sleep tonight because I am so high but then I will want to sleep for 24 hours tomorrow.
"I am adamant that the ball was not out, but having said that I think we were the stronger and better side on the night and I don't care if we win the league or finish second as long as we are in the Premiership next season."
Wigan boss Paul Jewell did not dispute the fact that the ball seemed to have gone out of play, but was adamant that Stewart was offside.
"The linesman got it wrong, but the main thing now is not to feel sorry for ourselves," he said.
"We are all men and we have to take it on the chin, they got the goal and it gave them a lift, but they were still the stronger and better side on the night."