After a topsy-turvy game that saw both teams hold onto the lead, Steve Williams pounced inside the penalty area to make it five wins from five for the Shaymen.
However, Halifax battled back to find an equaliser shortly before the half-hour mark when Marc Roberts kept his composure in a pack of bodies to fire the ball into the net from inside the penalty area.
However, the league leaders attempts to extend their winning run suffered a blow shortly after the restart when Ben Tomlinson netted a penalty for Lincoln for his second goal of the season.
Lincoln almost took the lead soon afterwards when Jordan Burrow struck the post, but their hopes of registering an impressive win suffered a blow with 25 minutes remaining when Bencherif was dismissed for a second yellow card.
That proved to be costly for his team as, 11 minutes later, Halifax found the decisive goal through Williams, who capitalised on a mistake from goalkeeper Nick Townsend to head into the net.