Jason Pinnocks opened the scoring for the hosts with a header in the 21st minute before the Fizzers scored a spectacular equaliser.
However Jacobs Lambe scored to give Bedfont & Feltham the lead just before half-time and captain Luke Craigs' shot from the 18-yard line took a slight deflection off a Sandhurst defender to beat the keeper and make it 3-1.
The Fizzers then grabbed a goal back to make it 3-2, but Lambe then added his second before debutant Sam Pledger made it 5-2 minutes later.
With five minutes left on the clock Robert Jermaine scored his first goal for the club and another goal from new player Marcus Black rounded off the scoring.
Sandhurst return to league action with a trip to Ash United on Saturday, while Eversley & California visit CB Hounslow United.
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