Histon dominated the opening half, regularly pegging back the visitors and putting them under pressure with direct balls into the box. But clear chances on goal were few, their only shot on target being Andrews' 16th-minute goal.
Tim Sills' header could have allowed Torquay to regain their two-goal cushion, had he not put Kevin Nicholson's free-kick wide.
Wayne Carlisle also went close moments later as his shot was deflected to safety by Gareth Gwillim for the Gulls' first corner of the game.
The home side pushed for an equaliser in the closing stages, Mitchell-King's shot going just inches away from putting the Stutes into an extra 30 minutes.
But Torquay held firm to move to within 90 minutes of a return to the Football League.
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