It made it three wins on the bounce for Rob Hunter's side, and a first victory in four visits to Dennyfield.
Thackley's Luke Robinson came up with the first chance of the game on 8 mins with a curled effort over the bar, but Town went ahead two minutes later when Devonte Morton sent Mark Simpson racing clear of the offside trap to sidestep stranded goalkeeper Luke Wilson and fire home.
A couple of chances followed for the home side; Jordan Hines half volleyed over the bar after the ball was fed to him from the left, before Nicholas Matthews' strike from a narrow angle was also over. Morton was unlucky not to get himself on the scoresheet on 29 mins when supplied by Niah Payne's great foray to the byeline, his strike shaving the top of the crossbar. He had his goal five minutes later however to make it 2-0. Michael Thompson's delivery was headed on by a defender to Simpson who picked out Morton at the back post to head home.
Player-manager Pat McGuire's free-kick had to be turned wide by a defender on 36 mins, and then another set piece saw a corner kick played into the box for a Thackley player to shoot straight at Wells. The action then turned to the other end of the park; Morton fired well over the bar after good work down the right by Simpson, and then a familiar barnstorming run from Shaquille Clarke-Adams ended in the midfielder shooting across the far post from a narrow angle.
After being the better side in the first half, The Miners made hard work of it after the break, and their struggle for possession allowed an improved home side to try and find a way into the game. They got one back from a free-kick on 54 mins, Hines' 20-yard effort finding the bottom corner. Four minutes later Wells diverted wide a Matthews effort at the near post.
On 66 mins a Simpson header brought a good stop from Wilson after the striker was picked out by Morton's cross. Four minutes later Hines' turn and shot was saved by Wells after a dangerous run by James Ngoe, before Ngoe himself had good chance on a break forward, but his effort was straight at the Town stopper. Substitutes Aodhan Brownlee and Mark Ferguson almost combined on 84 mins for a Town third, but Brownlee's through ball was agonisingly just in front of Ferguson, allowing Wilson to claim.
The remainder saw the Dennyboys go in search of a late equalizer, but Wells wasn't tested and it was Garforth who finally made the points safe deep into injury time. Morton won the ball on the right wing and crossed to Simpson who coolly chipped defender and keeper to make it three. It was no more than the striker deserved after an excellent all-round display, and his partnership with Morton looks a promising one.
Town are next in action next Saturday when we visit Maltby Main (kick-off 3pm).