The former Newcastle winger curled home a stoppage time winner to seal a famous comeback for the Latics, who had entered the final ten minutes of the game at the DW Stadium two goals down.
Goals in either half from Theo Walcott and Mikael Silvestre looked to have secured the points for Arsene Wenger's men, only for Ben Watson and Titus Bramble to haul Wigan level.
And just when the drama looked to have ended N'Zogbia clinched a famous win from the edge of the box.
Wigan had the first sight of goal when N'Zogbia pounced on a Sol Campbell error, but could only fire over on five minutes.
N'Zogbia was at it again seven minutes later, but again after finding himself in space 18 yards out his effort failed to trouble keeper Lukasz Fabianski.
But Walcott gave Wenger's side a half-time lead when, put clear by Nicklas Bendtner, he nipped past Bramble and bobbled a left-footed shot past Chris Kirkland.
Wigan had a good shout for a penalty denied early in the second half as Samir Nasri appeared to have pulled back Watson.
And the Gunners rubbed salt into the Wigan wounds immediately by going straight down to the other end of the field and getting their second through Silvestre's 48th minute header.
With the home side looking dead and buried Watson got them back into the game by calmly slotting home from 12 yards with ten minutes remaining.
And in a frantic finale Bramble got his side level a minute from time with a close-range header after Fabianski had failed to catch a corner right under his own crossbar.
N'Zogbia then secured a potentially crucial three points by making space to curl an exquisite left-footer past Fabianski and in off the post from the edge of the box.