The talented Millfield all-rounder, who also plays off scratch at golf, took four wickets in his final over as Basingstoke were dismissed for 232.
Welsh (37) then shared a half-century opening stand with fellow teen Adam Cutler (26) before the young South Wilts side slipped to 157 all out.
Millfield's Director of Cricket Mark Garaway explained: "Will's in our 2nd tier team, who bats in the top four, bowls a bit and catches pigeons.
"His catching prowess earned him a call up into the Meyer’s XI during the recent cup run which took the side to Lords for the National Final. Will took four magnificent catches in the final four matches of the competition.
"I really like his bowling action, very fluid and we have been giving him more and more overs in the second half of the season, so it’s great to hear that he has taken that confidence into his club cricket."