Fish scored a total of 81 runs in an innings that included ten 4s and one 6 as Beverley chased down the required total with runs to spare.
Will Harrison was also in the runs as he helped himself to 67 runs before he was caught out off a delivery from Frinley Scott.
Beverley are at home again next weekend when they will face Ripon a side who a just 34 points ahead of Beverley in the Hunters Y&DSCL Division 1.
*Beverley Town (30) beat Heworth (5) by eight wickets
Heworth 185-7 (Joel Johnson 38, Tom Hodgson 32, Joey Franklin 3-60)
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