Garforth showed their typical "never say die" attitude and more, as they progressed from an incredible Emirates FA Cup preliminary round replay.
Heaton got off to a dream start when Konner Lamb struck a 25 yard shot into the top corner.
Seven minutes later the Miners were stunned when Daniel Stephenson curled home a free kick.
Jay Davis struck a typical wonder goal from 45 yards on 24 minutes to get Town back in it.
Max Tweddle struck from the spot four minutes after the break, but Joe Smith got his marching orders (for what was deemed to be a straight red card) and the match swung from end to end.
Either team could have snatched a winner in extra time, and Garforth were seemingly up against it when Jamie Barkway was given a second yellow card but substitute Charlie Marshall was the hero of the moment, lashing home the winner two minutes from time.
Garforth will now host Bury FC in the next round on Saturday 31st August.