Goals from Heidar Helguson and Joe Mason put Cardiff ahead before Charlton struck back through a Johnnie Jackson double and further goals from Dale Stephens, Danny Haynes and Rob Hulse.
Powell's side then survived a late rally as Cardiff recorded late efforts from Craig Noone and Aron Gunnarrson but they held on to claim a first home win since the second match of the season.
"It was an entertaining evening and a real lift for us, especially at home, as home is where you really want to get your points in front of your fans," said Powell.
"The crowd could quite easily have turned at 2-0 down but I felt they dragged us through and our support was superb.
"We had only scored five goals at home before tonight and now we have doubled it. We were 2-0 down and then you saw the resolve and character of the players, they showed a lot of heart.
"We lost heavily on Saturday (a 4-1 home defeat to Middlesbrough) and had a few days of soul searching but they got themselves back in the game. The first 20 minutes of the second period we were devastating.
"Maybe we got a bit of luck we haven't had this year with Dale Stephens' goal but Rob Hulse and Danny Haynes deserved their goals.
"As a manager, I am not happy with goals against as that can count for an extra point, but it was a superb night for us."