Dany N'Guessan grabbed the decisive goal 10 minutes before the break when he headed home Johnnie Jackson's free-kick to ensure the Addicks maintained an eight-point lead over second-placed Sheffield Wednesday, who beat Oldham 3-0 at lunchtime.
Powell said: "It's a tough period for everyone and especially for us after going down to nine men on Saturday at Oldham, but still coming out with three points.
"It's always a tough ask to be ready for another League One club in less than 48 hours, but I thought the players were really gutsy, determined and we just hung in there because I thought Walsall contributed to a good game.
"They created some chances and the position they are in is wrong for them because they played some decent stuff.
"I thought Dany N'Guessan was a game-changer for us. He looked lively, obviously scored the goal, took some shots with his left and right foot and he effects the game. You are going to need people like that in games like this, where all you need are the three points."