The Hornets took an early lead through Daniel Pudil but were otherwise poor in the opening period and trailed at the break through a Tommie Hoban own goal and Yann Kermorgant's strike.
The Addicks rallied to take the lead again by midway through the second half thanks to an Almen Abdi penalty and an Alex Geijo goal, but Kermorgant turned home the equaliser before Johnnie Jackson sealed the points for Charlton 12 minutes from time.
Powell said: "We had a tough December - three draws, three losses - after having a very good November, so it's a real positive result for us and a good way for us to kick off the new year.
"It was a sensational game. Both teams played their part in what was a great game for everyone watching but I felt on the balance overall we just about deserved it.
"But they had some good chances, my keeper made a couple of good blocks, but overall we had 10 chances to their five and it was good that we took four of them."