Second-half goals from Powell and substitute Sam Baldock tightened the Dons' grip on a play-off place, while Paul Benson was sent off for the Addicks at the death.
The Dons dominated a subdued first half and Rowan Vine's 25-yard curler was saved at full-stretch by Ross Worner, who then showed good reflexes to keep out a sliced clearance from Benson.
Therry Racon had a 25-yard shot well-saved by David Martin as Charlton improved after the break but Powell capped a swift counter-attack to put the Dons ahead. Powell coolly slotted his ninth goal of the season underneath Worner from Luke Chadwick's unselfish square pass, after good work down the left by Baldock.
Dons skipper Dean Lewington curled a free-kick against the post late on before Benson was shown a straight red card for a rash tackle on Stephen Gleeson.
Baldock sealed the win in the sixth minute of stoppage time, tucking the ball into the corner of the net at the second attempt after his initial shot had been blocked.