Roberto Martinez's side scored twice in the first eight minutes and although Arsenal struck back quickly at Emirates Stadium, Wigan hung on to claim a victory that moved them five points clear of relegation with four matches left in the season.
Arsenal stayed third, five points ahead of their North London neighbours Tottenham Hotspur and fifth-placed Newcastle United.
"I am so so satisfied because this wasn't an accident," Martinez told Sky Sports. "The manner in which we coped physically and tactically makes me very very proud.
"It was a well deserved three points and to say that speaks volumes about the performance of my players."
Wigan, who beat league leaders Manchester United 1-0 last week, took the lead when striker Franco di Santo scored a classic counter-attacking goal after seven minutes and they immediately doubled the advantage through Jordi Gomez.
Arsenal, who had won nine of their last 10 league matches, were shell-shocked but they regrouped quickly and defender Thomas Vermaelen powered home a header after 21 minutes from Tomas Rosicky's whipped cross.
The hosts continued to dominate possession and Wigan goalkeeper Ali Al Habsi made several fine saves to keep his team in front at half-time.
Wigan defended bravely in the second half as Arsenal's frustration mounted and the visitors' man-of-the-match striker Victor Moses wasted a good chance to add a third goal after breaking clear of the home defence.
"We should have been ahead at half-time but in the second half we did not create a lot because we were not patient enough," Arsenal manager Arsene Wenger said.
"In the second half we lost our cohesion, we were doing too much individually, the passing wasn't quick enough to be dangerous. We had too many strikers, we were exposed a bit but we weren't sharp enough."
Wigan climbed three points ahead of 17th-placed Queens Park Rangers and five clear of Bolton Wanderers who occupy the last relegation spot but have two games in hand on their rivals.
