Garforth almost clutched a draw from the jaws of defeat, but Golcar held out for the win on a freezing night in Huddersfield.
The home side came flying out of the blocks and led 2-0 at the break.
When a neat left footed free kick made it three, it seemed to be contest over, but Town rallied late on, scoring twice, to set up a thrilling finish tk the match.
Golcar managed to hold on through four minutes of added time to claim three points.