Halifax started the better of the two sides and enjoyed two good chances in the opening seven minutes when Wayne Jacobs fired a shot wide before Lewis Killeen drove a close-range effort past the post.
Stevenage, who made little impact in the opening exchanges, took what proved to be the decisive lead after 23 minutes. Darryn Stamp was the provider when his neat through ball split the Town defence and Anthony Elding raced clear to drive the ball past Ian Dunbavin.
The goal lifted Stevenage, they went on to dominate the rest of the first half with Stamp and Dannie Bulman both coming close to adding a decisive second.
The second half began in similar fashion with Stevenage dominating the game, but it turned on 56 minutes with the introduction of Justin Bowler and Chris Senior in a Halifax double substitution.
From this point on the Shaymen took a grip of the game and had two clear cut chances to find the back of the net.
Senior forced a stunning tip-over from Alan Julian on the hour mark while five minutes later Martin Foster drove a free- kick against the woodwork only for Halifax to see a shot from the rebound cleared off the line.
Stevenage made defensive substitutions in the final ten minutes and sat back to claim three points which keep up the pressure on table topping Grays.