Nicky Butt's young side were good value for another victory against an Evo-Stik Premier Division team that contained former Reds apprentice Kenny Strickland at right-back.
Wilson took only three minutes to open the scoring by latching onto a through ball by Sam Byrne and firing a low shot past Zac Hibbert in the home goal. The keeper made a good block to deny Wilson a second when a goal seemed certain before Jack Barmby unleashed a long-range effort that whistled wide.
Skem held their own with some neat close passing as right-winger Matty Hughes impressed with Kevin Leadbetter closest to scoring for them in the first period when lifting his shot over the bar. However, it was 2-0 moments later when Hibbert kept out a Wilson shot but Rudge pounced to tap into an empty net.
Wilson departed the action at half time and Skelmersdale carved out the better chances with Hughes and Joe Holt seeing shots blocked and the same players bringing the best out of Jonny Sutherland soon afterwards. Leadbetter lashed a free-kick over the top as heavy showers poured down and Peter Wylie pulled a goal back from close range after Tom Hardwick headed on a corner.
Substitute Ashley Fletcher lobbed wide before Holt's cross-shot came closest to levelling the scores when it flashed past the far post.
The Reds are also in action on Thursday against Trafford FC at Shawe View.
United: Sutherland; Weir, McNair, Grimshaw, Rowley; Barmby (Harrop 73), Rudge, Pearson, Rothwell, Byrne (Fletcher 63); Wilson (Adarabioyo 46).