The Pitching In Northern Premier League Premier Division side defeated York City 1-0 to progress to the second round of the tournament for the first time since the 1958-59 season.
Striker and former Italy Under-20s international Diego De Girolamo scored the only goal of the fixture, netting in the 85th minute in front of more than 1,000 travelling supporters at the York Community Stadium.
Buxton, who are the lowest ranked team remaining in the competition, will host Morecambe on the weekend of December 4 in the next round.
Winners will be rewarded with £34,000 of prize money, as well as a spot in the third round draw alongside Premier League and Championship clubs.
Keep up-to-date with our exclusive email newsletters.
Subscribe