Man of the match Kevin Terhaerdt was also the match winner with a goal late in the first half on a wet and windy night at the Bannister Prentice Stadium.
Staveley threw everything at Garforth in the second half, but the Miners held firm to to take three points and extend their unbeaten league run to eleven games.
Kevin was awarded man of the match by match sponsors Wharfeside Hire.
Report and highlights to follow.
Town are next in action at home to AFC Mansfield on Saturday, kick-off 3pm.