Jonathan Obika was on target six minutes into overtime as the Addicks moved towards mid-table safety after making it seven points from three games in eight days.
Johnnie Jackson fired Charlton in front on 47 minutes before Luke Varney equalised nine minutes from time.
However, Obika sealed the points and Powell said: "I'm really pleased with the whole week, ecstatic with the performance today as we didn't deserve to be at 1-1.
"It has been a pivotal week, to get seven points and a real gritty, dogged point at Brighton.
"We have to do these things to survive in the Championship. And there's no better way of winning than in the last minute.
"We knew we had that tag of least home wins but that's gone now.
"Our away form has kept us going, and during the international break I thought that we had four home games we could win.
"To beat Leeds today was fully deserved and any point in the Championship is massive.
"I don't want our players relaxing. I've set them no targets."