Leonardo Ulloa had put Brighton in front on 22 minutes with a low finish from 10 yards.
But Charlton levelled on 31 minutes through Wilson, and he then fired the Addicks ahead on 56 minutes.
Yann Kermorgant's free-kick made it three 15 minutes from time, before Ulloa pulled one back in stoppage time for the Seagulls.
But the Addicks held on for the third home victory of the season, and Powell was thrilled with the contribution of Wilson.
"They were two excellent finishes and he deserved that for his whole performance," said the Addicks boss.
"He's OK in front of goal, I like him in those positions and they were quick finishes.
"Like most players he is quite instinctive when he is in those areas.
"I felt for his efforts, athleticism, diligence he was rewarded with not just one but two goal and he finished them really well.
"I'm really pleased for my group of players and especially our fans," added Powell.
"I felt there was a real positive energy from the players and supporters. Even though we went behind and we were playing against a very good side, who tend to dominate possession.
"We kept our composure and deservedly got an equaliser and performed heroically. There were some big performances from my players.
"This is a big period for us with lots of games in a short period of time."
Brighton assistant manager Nathan Jones was left to reflect three cases of poor defending as Albion conceded three times for the first time in the league this season.
He was however pleased by the return of striker Ulloa, who made his first start since October.
He said: "Leo is an excellent player, Ashley Barnes had done fantastically well in his absence, but we have got him back and now and we have got added competition.
"We have missed Leo because he was our top scorer when he got injured, and he has returned to that now by scoring two today.
"We had enough chances to have got something from the game. Charlton set-up well took their chances, but sadly we didn't take ours.
"We got the first goal early, which was pleasing but then we didn't really go on from there, that is the most disappointing thing.
"It's one of those things. We have been excellent for the last 10 or 11 games, and we haven't conceded three since the Capital One Cup defeat to Newport.
"It is a little bit out of character for us and the pitch made it very difficult in terms of trying to play fluently."