Scott Cuthbert and Billy Paynter added Swindon's other goals before Chris Palmer scored a late consolation for the visiting Gills.
Wilson said: "I was very pleased with the way we played, we played with confidence. It was a great strike by Charlie, he had no space to work in but turned well and the keeper didn't see it go in. He only trained for one day earlier in the week.
"On the downside, Alan Sheehan could be out for four to six weeks (with a pulled hamstring). But we will be trying to get two or three players in, possibly by the Stockport game on Tuesday, but we should have them against Leeds on Saturday."