He went up for a right-wing cross from burly defender Steve Evans and headed past Stevenage keeper Alan Julian, who got fingers to the ball but couldn't keep it out.
Borough were up against a well-organised defence and faded after a bright start before staging a late rally that nearly earned a replay.
Their tall substitute Luke Oliver side-footed a pass that put fellow sub Craig Dobson in space and unmarked, only for him to waste the opening with a hasty shot that flew wide.
Earlier Steve Morison tested home keeper Mike Ingham with a glancing header from George Boyd's cross. Boyd had the next opening, latching on to a pass from Jon Nurse, but shot wide. Late headers from Nurse and Morison were headed away for corners.
Wrexham generally had more attacking ideas and Danny Williams was only inches too high with a header from Darren Ferguson's 20-yard free-kick.
Another Ferguson free-kick picked out Evans, whose power header forced Julian to make a fine save.
The Borough keeper also kept out shots from Mark Jones, Matt Done and Lee Roche but lone striker Maheta Molango fluffed two gilt-edged openings, shooting wildly over the crossbar.