The Charlton forward saw his deflected shot off Robert Kiernan beat the dive of Latics goalkeeper Scott Carson in the third minute of injury-time at The Valley.
Charlton and Wigan had looked set to secure a share of the points for the second successive weekend before Moussa struck.
Jordan Cousins fired the Addicks ahead before Callum McManaman levelled for the visitors.
Wigan, tipped as one of the favourites to win promotion to the top-flight, started brightly with winger McManaman lively down the right flank.
But Uwe Rosler's men were rocked in the eighth minute when Charlton went ahead courtesy of a superb strike by Cousins.
The England Under-21 midfielder collected Johann Gudmundsson's pass, cut inside Ivan Ramis and his well-struck shot arrowed into the top corner beyond Carson.
Yet Wigan responded in the right fashion as McManaman equalised in the 22nd minute.
James McArthur, who started after Wigan turned down a £4million bid from Premier League newcomers Burnley, provided the assist for the winger.
McManaman turned Charlton full-back Rhoys Wiggins inside out and directed his left-footed effort neatly past Stephen Henderson from an acute angle.
It was Wigan's first goal at the Valley in the fourth meeting between the clubs in south London.
Wigan left-back Andrew Taylor was booked by referee Andy D'Urso for a foul on Gudmundsson, but the visitors were growing into the contest.
Emyr Huws, on loan from Manchester City, fired a long-range shot over the crossbar, but the intent was there.
This was an entertaining encounter and Bob Peeters' Charlton side created chances of their own.
Cousins supplied Wiggins and the left-back saw his shot well saved by Carson.
Rosler made a change at the interval, introducing Shaun Maloney for the ineffective Riera.
But Charlton continued to threaten through the impressive Gudmundsson, whose shot was easily handled by Carson.
Then Carson was forced into action in the 55th minute when Igor Vetokele's burst left Ramis trailing and his shot was deflected off James Perch which needed the smart reflexes of the England keeper at his near post.
Moussa was brought on by the home side for the industrious centre-forward George Tucudean, but there were not too many goal-scoring opportunities of note.
Charlton were dealt a blow when goalkeeper Henderson limped off injured with 22-year-old Nick Pope, with just one previous appearance for the Addicks, drafted into the fray.
The hosts should have sealed maximum points in injury-time when Vetokele skinned Spanish centre-back Ramis once again, but saw his shot superbly saved by Carson before Moussa had the final say.