Fisher missed out on a tie with rivals Stansfeld after losing 2-1 to Badshot Lea in the first round of the FA Vase last weekend.
The Combined Counties Premier Division South side took the lead at St Paul’s through Tane Caubo who pounced on the loose ball after goalkeeper Dan Carpanini had made a save.
Michael Sarpong, who had been on the wrong end of a bad challenge before continuing after treatment, levelled for the hosts with a brilliant strike in front of an attendance of 162 in Rotherhithe.
But the home fans were quietened again when Caubo scored his second in the 61st minute.
Christian Udo had a late chance to equalise but Badshot goalkeeper Kallum Lunn saved as his side went through to the second round.