Stourbridge led 3-0 with ten minutes to go, and looked comfortable even though it was a far from commanding performance against dogged opposition.
But the Bucks netted what appeared a consolation eight minutes from time, and then another as they game entered the added period. And they were mighty close to snatching a draw at the death, with a header against the bar and then a follow-up header put over with the goal gaping.
There was little hint of the late drama early on as Luke Benbow repeated his free-kick exploits of Monday night, this time placing the ball in the opposite top corner on 12 minutes to put the Glassboys ahead, whilst Jordan Archer saw his shot saved by Jan Budtz late in the half. There was also a lengthy delay in between times as the referee went down with cramp and a replacement official was sought.
Buxton had the better of the opening stages of the second period, before Benbow doubled Stourbridge's lead out of nothing. Taking the ball down and turning his man some 35 yards from goal, he looked up and fired first time over the backpedalling Budtz for a spectacular goal.
Kayelden Brown seemed to have wrapped up proceedings 17 minutes from time as he bundled home from Jake Heath's cross, but Bradley Grayson found space in the area on 82 minutes to tuck home a smart finish, and then tapped home another from a corner to set up a grandstand finish in which Jamie Jackson almost pinched a point for his team.