The youngster capitalized on a loose clearance, scoring from 30 yards with an audacious lob over the stranded goalkeeper.
Williams also registered an assist, helping Cheltenham climb to 11th in League Two after their emphatic victory.
"I'm really happy to score and help the team get three points. I've been working hard to try and impress the gaffer, to try help him give me the opportunity, and thankfully he has," Williams told Cheltenham club media.
"We can hopefully push for the play-offs. I had no idea how I put it on a plate for him (the assist), I just tried to put it in an area, but I was chuffed we scored because we were under the cosh.
"The goal was top, I ran straight to the fans. A top moment for me and my family watching, so I'm really happy with it. I just took a quick glance and saw the goalkeeper off his line."