Jos Millar grabbed a first-half brace after the Moles had fallen behind.
And Jemel Johnson capped a fine performance with the winner 10 minutes from time.
Louis Cordice and Stuart Macllelan scored for Flackwell.
Elsewhere in the division, Wokingham & Emmbrook made it two wins from two games thanks to a 3-1 victory away to Kidlington.
On the scoresheet for the Satsumas were Chris Wateridge, Luke Lee and Callum Eagle.
Lee Boon's 63rd minute goal was enough to send Ascot United through to the second qualifying round of the FA Cup at the expense of Slimbridge.
Bracknell Town survived a last minute penalty miss by Easington Sports to come away with a 3-2 win.
The Robins came from behind twice to earn the three points.
Sam Barratt headed in Bracknell's equaliser in the first half, and then he found Wayne Carter as Bracknell made it 2-2 after the break.
Substitute Reece Jacques gave the Robins the lead on the hour mark but it was a nervy ending to the match when Easington were awarded a penalty deep into stoppage time to level the scores, but their striker fired wide.
Eversley played the last 20 minutes of their match with 10 men but emerged as 4-3 winners over Spelthorne Sports in Combined Counties Division One.
* For the best local football coverage, see Thursday's News.