Lee Tomlin gave Peterborough the lead after 29 minutes but Johnnie Jackson headed Charlton level in the 57th minute.
Two minutes later Bradley Wright-Phillips made it three goals in as many games to put Charlton in front and Kelvin Langmead's own goal made it 3-1 before Craig Mackail-Smith pulled one back late on.
The win continued Charlton's 100% record since Powell took over and he said: "We kept calm because the first half was all Peterborough. To be fair to them they were excellent.
"We didn't start so I basically said to the boys at half-time: 'This is where we turn up.'
"I'm extremely pleased we've kept this run going. We've won and got three points and that is all we can do because the teams in and around us have won again but it is up to us to do what we have to do."
Source: PA
Source: PA