A disastrous start to the game for Garforth saw the hosts, who'd failed to score in their last four games, go two goals up.
Alfie Docherty cut inside from the left and, spotting Harry Flatters' near post unguarded, tried his luck from 30-yards and scored with a low strike into the bottom corner.
On 13 mins the lead was doubled when a cross was half-cleared to Matty Willshaw who slammed the ball high into the net.
Five minutes later there was almost a Town own goal to make it three when Alex Payne's corner kick was headed narrowly wide by a Miners defender. Joe Fergsuon then came close with a 25-yard effort which Flatters palmed wide.
Garforth did a little better towards the end of the half if not managing a shot on target. Oli Patrick shot over the bar on 35 mins after a Mutty Al-Jahadhmy run from out wide. That said, Willshaw probably should've made it three on 43 mins when firing wide Ferguson's assist.
Town's task was made even harder moments before the break when Patrick was sent off for a bad challenge on Ferguson.
The ten men managed to create a little bit more in the second half, but quality in the final third was lacking and the sort of comeback seen against Grimsby or Consett never looked likely.
Another good chance for Willshaw, who should've had a hattrick, came on 51 mins when he pounced on a Garforth error but could only lash against the side netting. Another chance for the striker saw him sky over the bar Payne's delivery.
On 59 mins a Charlie Marshall header from a free kick brought a routine save from Guisborough keeper Ryan Catterick, then down the other end Matty Tymon's diving header from Kallum Griffith's cross went wide.
On 71 mins Charlie Marshall's free kick was pushed away by Catterick but with nobody in Town colours to capitalise.
In terms of chances created that was pretty much that and The Priorymen went on to celebrate victory in this first competitive "all GTFC" clash, and the first game this season in which we've failed to score.
A bad day at the office for Paul Marshall's depleted side who head up to Northumberland on Saturday for a visit to Blyth Spartans (kick-off 3pm).
Town team: Flatters, White (Burgess 58), Tweddle (Jeff 76), O. Marshall, Zachariou (McGrath 46), Emery (c), Eggleston (McAleese-Shorney 71), Allerton (M.F. "Mutty Junior" Al-Jahadhmy 54), C. Marshall, Patrick, M. Al-Jahadhmy.
Cautions: C. Marshall 69, "Mutty Junior" 90.
Sent off: Patrick 44
Attendance: 255.