AFC Wallingford went behind after just two minutes of Saturday's Combined Counties match, but then dominated for the remaining 88 minutes to run out comfortable winners.
Reed saw his speculative shot from 25-yards skid off the wet ground and beat Rutherford to put the visitors ahead.
Mick Mulvaney levelled things after ten minutes when he shot home after a Barry Primmer pull back.
Andy Shildrick then put Wallingford ahead when he headed home an Ian Concannon cross.
Concannon then made the game safe when he was on hand to slot home after a Pete Bryan shot rebounded to the former Oxford United striker off Wells.
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