Danny Swanson had given the home side a first-half lead before two goals in four minutes from Johnnie Jackson and then Danny Haynes put the visitors ahead.
Peterborough earned a point 20 minutes before the end though Michael Bostwick.
Chasing their fourth league win in six outings, Posh were without the services of injured loan trio Alex Pritchard, Scott Wootton and Davide Petrucci.
Chris Solly returned for the visitors but Dale Stephens missed the clash, along with suspended striker Yann Kermorgant.
And it was Charlton - who had won seven times on their travels going into the fixture - who were first to threaten.
After only four minutes a cross by Haynes was met by Lawrie Wilson who stuck the crossbar with his 15-yard effort, before Ricardo Fuller also went close.
Chris Powell's side had taken early command against the strugglers and Fuller also went close barely two minutes later before Haynes saw another effort from distance caught by Peterborough keeper Robert Olejnik.
Posh had failed to fire but after Gabriel Zakuani had shot over from just six yards, the hosts took the lead after 24 minutes when Swanson hit home from 18 yards for his first of the season.
It was a measure of Peterborough's recent improvement that they could withstand early pressure before making an impact on the break, and they visibly grew in confidence after drawing first blood.
Ten minutes from half-time they could have made it two when Nathaniel Mendez-Laing's 12-yard try was saved by an alert David Button in the visitors' goal.
The Valiants could consider themselves unlucky to be a goal down but Powell called on his men to concentrate towards the break as another Posh goal could have decided their fate.
And the hosts nearly got it within a minute of the restart when a 12-yard effort from Lee Tomlin struck the post with Button beaten.
Charlton had their backs to the wall but they were level after 55 minutes when Callum Harriott supplied a pass to Jackson who despatched with ease from 12 yards out.
Within four minutes Powell's men had turned the game on its head. This time Haynes got on the end of a Michael Robinson header to head home emphatically from six yards out.
Posh were now forced onto the attack and Button had to be alert to save an effort from Dwight Gayle from 18 yards.
But the hosts levelled after 71 minutes when Michael Bostwick hammered in an effort from all of 25 yards to leave Button helpless.
Charlton came closest in the closing stages but Button tipped over Jackson's 30-yard free-kick as the honours finished even in a fair result.