Marvin Sordell gave Charlton a dream start just minutes into the match when he took advantage of poor defending to slot home and put the visitors in front.
Charlton, however, came closest to adding to the score when Reza Ghoochannejhad's volley hit the underside of the bar.
McManaman then curled an effort of his own against the woodwork just before the break.
Nicky Maynard had the ball in the net minutes after the restart, but the goal was ruled out for offside.
Wigan grew in confidence as the half went on, with Emmerson Boyce heading Ben Watson's free kick just wide.
Fortune latched onto Josh McEachran's through-ball two minutes from time to equalise, before Jordi Gomez curled in a free kick to give the Latics all three points.