Danny Spencer added a second from a free-kick before Louis Briscoe pulled one back for the visitors.
A late Tom Berwick effort from close range sealed the victory for Kevin Wilkin's side, who next face Leamington at the New Windmill on Saturday.
Bedworth United, beaten by Nuneaton at the weekend, were thumped 5-0 by Hinckley United at The Oval.
Source: BBC Sport
Source: BBC Sport