The on-loan Brighton striker stroked in a 65th-minute penalty to hand the Addicks their first win in four games and deal another blow to the Dons' slim play-off hopes.
The hosts controlled the early exchanges and skipper Dean Lewington headed Peter Leven's free-kick straight at keeper Darren Randolph from seven yards before blasting a 30-yard rocket just over the crossbar.
Luke Chadwick drilled a low shot inches wide from distance, while David Mooney scuffed Charlton's first chance straight at Willy Gueret from Forster's cut-back. Gueret then produced a good diving save to keep out Therry Racon's low 15-yard strike before Jermaine Easter's fierce snap-shot was beaten out by Randolph at the other end.
Charlton piled forward after the break and Forster's confident penalty put them ahead, after he had been tripped in the box by Sean O'Hanlon's needless lunge.
The Dons pressed for an equaliser late on but Randolph saved a close-range header from O'Hanlon - who was stretchered off with a recurrence of his knee injury - and then superbly denied Easter one-on-one.