Jamandhi Henry fired Bedfont through to the second qualifying round of the FA Vase on Saturday.
Henry netted the winner after visitors Ampthill Town had equalised Mark Gallagher's opener for the Orchardmen.
Bedfont, who drew 1-1 with Chessington & Hook in the Combined Counties Premier on Tuesday night, will now take face Codicote, of the Herts Senior League, in the next round on Saturday week.
Before that, they visit Raynes Park Vale on Saturday, and host Camberley Town on Tuesday, in the league.
However, Feltham failed to make it past the first qualifying round after going down 4-0 at Rushden & Higham United.
They will be looking to bounce back when they welcome Worcester Park in Combined Counties One on Saturday.
Bedfont Green will have to wait longer to find some 'bounce-back-ability' following their 3-0 defeat at Cove in the Combined Counties Premier as they have no game this week, due to opponents Colliers Wood United being in FA Cup action.
Also in cup action were CB Hounslow United, who will have to replay Guildford City following a 3-3 draw in the Premier Challenge Cup first round.
CB came from 2-0 down to draw level through an Anthony Bridgeman brace, then took the lead in extra-time through Michael Hinckson, but conceded again in the final minute of the added 30.
They host Farnham Town on Saturday in Combined Counties One , while leaders Hanworth Villa travel to second-placed Sheerwater on the back of an 8-1 thrashing of Chobham.
Brothers Lee and Darren Higgs did the damage for Villa, with Lee hitting a hat-trick and Darren bagging a brace. Matt Grave also chipped in with two, while Daryl North notched one too.
Villa's Southern Combination Cup game against Knaphill on Tuesday night was postponed.