Louis Reed's goal in the 80th minute at Turf Moor completed a comeback 2-1 win for the League One team in the fourth round after they'd gone behind in the first half on Saturday.
As giant-killings go, it might not be as spectacular as non-league Macclesfield Town's victory against title holders Crystal Palace last month - but it is another major shock result in soccer's oldest knock-out competition.
"As soon as it left my boot I felt it going in," Reed told the BBC.
"I have been working on them throughout the week. The lads said, 'This is your moment, go and take it'. Thankfully, I did."
Mansfield are mid-table in League One and even against a Burnley team that had won just two of their previous 18 games, and deep in the relegation scrap, went into the match as underdogs.
And when Josh Laurent scored in the 21st, it looked like the hosts would book their place in the last 16.
That was until a second-half fightback from Mansfield sparked by Rhys Oates' equaliser eight minutes after the break and Reed's late winner.
"We have lost a game of football today against a team we should be beating," Burnley manager Scott Parker said.
"When I analyse the game, we missed too many chances today - glorious chances where we could have put the game out of sight. We weren't clinical enough ... and while it stays at 1-0, you are always on an edge and that was proven today."
It's been a very good week for Pep Guardiola's Manchester City who've closed the gap on Premier League leaders Arsenal to four points and got past local fourth-tier rivals Salford City 2-0 to make the fifth round.
City beat Exeter 10-1 in the previous round and Salford might have feared a similar outcome when Alfie Dorrington scored an own goal in the sixth minute, but City had to wait until the 81st to score again through Marc Guehi.
Liverpool's Premier League title defence may have unravelled, but Arne Slot's team are through to round five with a 3-0 win against Brighton & Hove Albion.
Goals from Curtis Jones, Dominik Szoboszlai and Mohamed Salah from the penalty spot ensured a comfortable win at Anfield.
Elsewhere, Socceroo Mohamed Toure got on the scoresheet again as Norwich City beat West Bromwich Albion 3-1, before Newcastle United won by the same scoreline at Aston Villa.
Burton Albion, fighting against relegation in the third tier, went toe-to-toe with top-flight West Ham United but went down 1-0, while Southampton also needed extra time to beat Leicester City 2-1.
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