Bury's Ryan Lowe grabbed his seventh goal of the season but Charlton came from behind to claim the three points.
Lowe, making his 100th Bury appearance, fired home a free-kick from 30 yards after Michael Morrison had fouled him.
Paul Hayes equalised for the Addicks, heading down into the net following a looping cross from Johnnie Jackson.
Lowe volleyed wide, but unbeaten Charlton then scored the winner when Jackson came in at the back post to convert from Dale Stephens' low pass.
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Bury manager Richie Barker told BBC Radio Manchester:
"I'm not saying we lost our way a little bit but that goal changed the game four minutes into the second half.
"It's hard mentally for these players when you keep going a goal up and we've got to be able to kill games off.
"Maybe we didn't create enough, but you're not going to create loads against the team who are sitting top of the league."
Charlton boss Chris Powell told BBC London 94.9:
"I'm extremely pleased because we set our standards this season and it's very early but its important because it breeds confidence.
"Positive results are what any football team needs. In the first half we didn't turn up and that wasn't us at all.
"Bury are a decent team, they like to pass the ball around and our game plan was to be patient."