Portsmouth's pressure had paid off five minutes before the interval when Andrés D'Alessandro fired them into the lead with a spectacular effort and Charlton were booed off at the interval.
The Addicks looked little better after the break, then suddenly upped a gear and turned the game on its head with goals from Bryan Hughes and Darren Bent in the last 14 minutes.
After the equaliser Charlton went to three at back with Herman Hreidarsson pushed up front and he set up the winner for Bent seven minutes from time as Charlton held on to secure the points.