Halifax earned their first away win of the season but they did it the hard way after battling for almost an hour with just ten men following the sending off Shaun Garnett.
The Shaymen defender was sent off for a handball after 32 minutes when he pushed the ball away from the line after keeper Tom Morgan had done well to push away a Kirk Jackson header.
Garnett got his marching orders and Stevenage skipper Jason Goodliffe took the resulting penalty but after forcing a fine save from Morgan and seeing a header from the rebound go over the bar, it was clear Stevenage had failed to take advantage of the turning point in the game.
Had Goodliffe managed to find the net it would of pulled the home side level as they were already a goal behind to a strike which Halifax had been threatening for some time.
Craig Midgley put the visitors ahead after 21 minutes when he converted from close range after an Ian Fitzpatrick had only half cleared.
It was a strike Halifax deserved and they should have netted earlier when Garnett someone managed to head over the bar with the goal at his mercy following a right-wing cross from Simon Parke.
Yet Stevenage where unable to make the extra man count, but they penned Halifax back for the entire second half and deserved to find a way back in the game.
Boro's Robin Trott looked to have levelled after 58 minutes when he saw a goalbound header cleared off the line by Parke and just three minutes later Jamie Campbell's shot at goal from the left flank which hit the post and out to safety.
Under-fire Boro boss Wayne Turner rang the changes by bringing on three subs and ended the game with four strikers on the pitch, but despite their upper hand Stevenage fell to another home defeat and have now won only once at Broadhall Way in seven games this season