The 20-year-old midfielder signed non-contract terms with the club just last week after being released by Chorlton.
Long struck just 16 minutes after joining the action as a second half substitute he collected a pass from Mike Edwards and coolly rounded goalkeeper Michael Ingham to slot in the decisive goal.
Wrexham, who were top of League Two after the opening round of games on Saturday, has dominated much of the second half, and could have gone behind but for a magnificant display by Michael Ingham between the posts.
County were strong at the back and despite Wrexham's superior possession, the north Wales side failed to penetrate the defense.
A goalless draw seem a cert until Long scored his first goal in the dying minutes of the game.