Unmarked Stamp, who joined the club recently and scored twice on his debut in a 3-1 win over Farnbrough last week, headed Jon Brady's curling cross straight at keeper Ian Dunbavin from close range.
Former Scunthorpe striker Stamp - who had a loan spell at Halifax as a youngster - did not do too much else in an anonymous display.
But the one glorious change he had would have sealed a stirring come back for the visitors who got back into the game through substitute Dino Maamria's near post drive on 73 minutes.
After that, Stevenage piled forward in search of an equaliser with more changes made by manager Graham Westley eventually leaving Boro with four strikers up front.
The tactical switch nearly paid off and fellow substitute Simon Weatherstone volleyed inches wide of the target from another Brady cross just minutes before Stamp fluffed his easy header.
Two early afternoon downpours plus an overnight deluge left the game in doubt, but Derbyshire-based referee Robert Shoebridge ruled the pitch was playable.
The surface cut up badly in places as the match went on and the condition ensured both sides could play little passing football.
Mr Shoebridge also showed good sense throughout the game by only issuing yellow cards for fouls committed with genuine malicious intent rather than for ones that were down to the conditions.
Halifax took the lead on 22 minutes with a Craig Midgley penalty awarded after Ryan Sugden was shoved in the back by Jason Goodliffe.
Sugden had a great game and was twice denied by Stevenage keeper Shaun Marshall in the first half. He also hit the post with another effort in the second half.
Dean Howell secured Halifax's 10th win on the season after side-footing Sugden's byline cross into the net on 52 minutes.
Play-off chasing Town have moved up to fourth in the Conference table and still have a game in hand on some teams.