Bell (10) and Middleton (18) steadied the ship and Purbrook reached 92 all out.
Ben Jones got an early break through when the visitors replied, but after that the match drifted away from Purbrook.
Wayward bowling and poor fielding allowed Fareham to win by 7 wickets in the 18th over.
Purbrook: S.Figgins, B.Jones, B.Thomas, T.Jones, H.Haran, H.Bell, P.Middleton, S.Bennett, M.Colban, S.Spencer, I.Budd.