Report: How Buxton FC finally ended their seven game search for a win
But the win came at a cost with the added-time dismissal of play-maker Tommy Elliot meaning he will likely be out of next week's six-pointer versus South Shields.
The high tension of the closing minutes was in marked contrast to the earlier part of this wind-blown but entertaining encounter which had been dominated by the visitors with the reward of a 2-0 lead.
Buxton's lead was well-deserved, as immediate control was established all over the pitch and that was maintained throughout the game's first quarter in particular.
Though facing the corner-to-corner gale, 'keeper Theo Richardson had little to do as the recently re-shaped defence in front of him was sound, with Ben Turner especially prominent and adept both in the air and on the ground.
Another factor was the superb midfield display of the re-called Lindon Meikle who did much to break up the Hyde United play and then begin visitors' attacks, which were frequent but lacking penetration as Jamie Ward, operating on the left, was for once little involved.
Buxton's efforts closest to scoring were a glancing header wide by Dan Cowan from an Elliot corner and a curling, 20-yard effort by the highly industrious Chris Dawson that was tipped over the angle by 'keeper Joe Green.
But the Bucks started the second half dynamically with two goals inside five minutes, promising a comfortable victory.
In the 48th minute Jason Gilchrist ghosted into the near-post area and touched home a low, right-flank cross for his first Buxton goal.
The visitors went close again from a Ward cut-back moments later.
But they soon made it 2-0 when a neat passing move towards the left flank culminated in Elliot feeding Warren Clarke, who offered a constant attacking threat, for a confident, 12-yard low finish.
More attacks followed as Buxton looked to kill the game off.
But they were put on the back foot in the 75th minute Jonah Mitchell halved the deficit.
Elliot was given a straight red-card in stoppage-time following a coming together with Krisel Prifti.