Buxton were denied a precious win last Saturday, after ten-man Frickley snatched a late equaliser.
Lee Morris opened the scoring after 15 minutes, but despite their dominance the hosts conceded in stoppage time.
It was the tenth goal that the Bucks have let in during the last ten minutes of league matches this season and the result means FC United, who Martin McIntosh’s side host over the Christmas period, move two points clear in fifth place in the Premier Division standings.
Against opponents who hadn’t won away from home all season, Buxton moved up the gears early on with Morris again the key man.
He pounced on a defensive error from the Frickley backline but his timid shot was hit straight at goalkeeper James Hitchcock.
The visitors then registered their first attempt when Gavin Allott, with 15 goals this season, showed his skill by beating three players only to see his effort fly just wide of Andy Warrington’s post.
Buxton then made the away side pay when Morris chipped the ball beyond Hitchcock for his 14th strike of the campaign.
The wind was playing havoc with both sides’ ability to retain possession and before the interval Warrington had to be alert after inswinging efforts from Frickley were heavily assisted by the weather.
Despite the wind getting stronger in the second half, it was Morris who had the first opportunity after the restart.
Skipper Steve Istead dipped in a cross but Morris’ header was straight at Hitchcock.
Efforts then followed from Thornhill and Morris again, but the hosts were struggling to build on their one-goal advantage.
Their next effort came from an unlikely source when Grant Black’s free-kick was helped on by the wind, only to cannon back off the bar.
The visitors were then reduced to ten men when defender Sam Denton lunged at Istead, earning him a second yellow in the space of three minutes.
Hitchcock then pulled off a terrific double save late on before the visitors struck deep into injury time.
A free-kick was punted into the Bucks’ box and after a knock-on, defender Jake Picton got the final touch to ensure another frustrating finish for McIntosh and his side.
Bucks: Warrington, Black, Palmer, Ryan, Green, Istead (Stevens 68), Niven, Harris, Thornhill (Reed 68), King, Morris (Johnson 90).