Despite Posh dominating much of the possession, Ricardo Fuller's moment of magic 13 minutes from time helped Athletic extend their unbeaten run to five matches.
The home fans went home happy as Yann Kermorgant tapped home a late second goal to ensure three points.
Charlton have now taken 13 points from their past five matches, which had propelled them up to 13th in the Championship and just five point from the play-off spots.
"There is going to be time when we are going to play better and not get much in return," admitted Powell after the game.
"I'll definitely take this. We've been thin on the ground at home, but we got a clean sheet.
"We have 13 points out of the last 15 so I can't complain. We've played better this year and lost so it is about time.
"Over the course of the season sometimes you might not merit the win, but because of your discipline and doggedness, which we needed this evening, you get wins."