The visitors, chasing a target of 248, seemed set for victory on 190-2, but a collapse saw them bowled out for 241 in the penultimate over.
Batting first, Aldershot made 247-7 in 52 overs thanks to 102 not out Ravi Gilbert. Leg-spinner Alex Gorton returned the best figures with 2-29.
Beaconsfield looked sure to chase this down thanks to Johnny Bowers, who hit 74 from 51 balls and supporting innings from Ed Barnett (51), Nilesh Odedra (33) and Zia Ashraf (30).
But Nick Biscontin (6-53) sparked a collapse that saw five wickets fall for 25 runs and the visitors fell just short.
This Saturday, Beaconsfield travel to Finchampstead 2nd.