Buxton recorded a first win in eight outings after coming out on top against ten-man Blyth Spartans last weekend.
The Bucks weathered a first-half storm before going 2-0 up thanks to Neil Stevens and Lee Morris.
Despite a late strike by Spartans’ substitute Craig Hubbard, Martin McIntosh’s men held on for a vital home win - their first in any competition since mid-October.
In the build-up to the game McIntosh challenged his players to an improved showing after they were knocked out of two cups in midweek.
They almost made an immediate impression just two minutes in when Morris controlled brilliantly in the area before somehow seeing his close-range effort sail wide of the right-hand post.
Blyth then upped the ante and a lashed effort from Paul Robinson, recently recruited from Darlington 1883, went just wide of the Bucks’ goal.
A lengthy stoppage in play then followed due to the Blyth goalkeeper Michal Misiewicz falling awkwardly after coming to claim a free-kick.
Morris then tried to profit from the goalkeeper’s knock when he fizzed a shot straight down the throat of the Greek stopper.
Robbie Dale, who had been a useful outlet down the left flank for Blyth, then curled an effort just over the bar after a wayward backpass from Carlos Logan was pounced on.
Sonny Andrews then had the final chance of the half but could only clip a shot over the bar to leave the visitors wondering how they hadn’t scored in the opening 45 minutes.
That profligacy proved to be vital come the second half as Buxton came out on the attack.
A double substitution by McIntosh, bringing on Spencer Harris and Mark Reed, saw an immediate spark for the hosts and it wasn’t long before the former made an impact.
Harris’ punt forward was spilled by Misiewicz and fell kindly to Stevens who prodded home his first of the campaign.
The hosts doubled their lead on 68 minutes when Morris capitalised on hesitant defending to slot home his 11th goal of the season.
Blyth sent on Ash Davis in a bid to get back into the game but within 15 minutes of his introduction he was shown a red card for an off-the-ball incident.
Despite the setback, Hubbard’s late, speculative effort proved to be merely a consolation for Blyth.
Bucks: Warrington, Black, Green, Istead (Harris), Palmer, Ryan, Thornhill, Stevens, Morris, Logan (Reed), King.