Buxton, who sit third in the Pitching In Northern Premier League Premier Division table, defeated National League North side Kettering Town 3-1 at home in a FA Cup replay following their 2-2 draw over the weekend.
The visitors took the lead through Kyle Perry on the 58th minute, before Ben Milnes drew level 15 minutes later to put the game into extra time. Diego De Girolamo helped the Bucks create history as his two goals secured a place in the next round, with 1,017 watching in the stands.
Club chairman David Hopkins said: "To see so many Buxton fans turn out in support of the team was amazing.
"Once again the players were outstanding and gave our fans a night to remember. It was particularly heart warming to see the pleasure given to our older supporters who have waited 59 years for us to reach the first round proper.
"We would encourage all those who must have enjoyed last night's game to continue coming to support the lads on what is proving to be an outstanding season in both league and cup."
Manager Gary Hayward commented: "It had everything: blood, sweat and tears. The lads keep impressing week-in and week out, running themselves into the ground and playing great football.
"The management team couldn't be prouder of them. As for the fans, they were in full voice behind the players and became our twelfth man. From top to bottom, everyone involved is part of the journey so far."
Buxton will face York City in the First Round Proper.
Elsewhere, Pontefract Collieries were knocked out of the cup by FC Halifax Town with a 1-0 score, Marske United fell to a 3-2 defeat away to Gateshead, York defeated Morpeth 3-1 and Paul Mullin scored twice for Wrexham in their 2-0 victory over Marine.
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