Charlton came into the match buoyed by a return of 10 points from their past four matches, which had propelled them up to 15th in the Championship.
Chris Powell's men impressed in the first half at The Valley but failed to take their chances, with Bradley Pritchard then hitting the post moments after the restart.
That header jolted Peterborough into life and they looked more likely to win until taking a sucker punch 13 minutes from time when Fuller fired in a fine effort from 25 yards.
Unfortunately the Jamaican had to be brought off immediately afterwards due to injury, but Charlton fans were soon cheering again as Yann Kermorgant tapped home a late second goal.
After Leon Cort did excellently to turn away an effort from on-loan Dwight Gayle at the other end, Arsenal's Frimpong again came close from distance as Charlton continued to press for an early opener.
Johnnie Jackson should have done better with a close-range header in the 17th minute, before Addicks goalkeeper Ben Hamer stopped a fizzing Michael Bostwick strike.
Peterborough ended the half on top and, after Gayle headed over a chance to mark his full debut with a goal, Hamer had to flick over a George Boyd strike.
Kermorgant sent a diving header wide shortly when the sides returned for the second half, before Pritchard's close-range header rattled the post.
George Thorne put wide and then Gayle was denied as Posh continued to threaten, before Boyd's shot deflected off Lee Tomlin onto the post.
The 518 visiting fans were in good voice and looked set to leave with a point or better until Fuller lashed home from distance five minutes later.
While the summer signing had to hobble off immediately, Powell's side were celebrating again five minutes from time when Kermorgant turned in substitute Danny Green's right-wing cross.