Batting first Bolton Percy set a total of 196 as that included a half-century from Ed Noble (54) and 40 from Matt Howden.
Mudd was the top wicket taker for Beverley finishing with figures of 4-66 while Jamie Roe 3-47 and Danny White 3-37 both enjoyed a fruitful day with the ball.
Defeat for Bolton Percy means they replaced Malton & Old Malton in the relegation places while for Beverley it keeps them at the right end of the table.
Beverley will be looking to continue their good run of form next weekend when they hit the road to face strugglers Malton & Old Malton.
*Beverley Town (30) beat Bolton Percy (7) by three wickets