Chasing the home side's total of 259-6, Beaconsfield fell just short on 252-7.
Choosing to bat first, Finchampstead were boosted by a brilliant 107 from 89 balls by Matt Keast, as Beaconsfield bowlers struggled on the flat pitch.
The visitors were given a fine start to their reply thanks to Zia Ashraf, with 87 from 112 balls and skipper Adam Francis (36).
But, thereafter, only David Heavyside, with 61 from 57 balls, made a sizeable contribution as Beaconsfield made it four games without a win.
They will be hoping to get back to winning ways at home to Fleet this Saturday.