Garforth were beaten in dramatic fashion after it looked like a late Nick Thompson goal had earned them a draw.
The Miners were the better side in the early exchanges, but Hemsworth took the lead through a breakaway goal, finished by Rhys Scott and ended the first half much stronger.
The second half was a scrappy affair and defeat looked on the cards until Thompson bundled the ball home in a goal mouth scramble.
Ben Gelder broke the visitors hearts with a 90th minute winner.
More to follow...