Morgan Parra's disastrous decision to take a tapped penalty rather than three points saw Clermont crash out of Europe against UBB, losing 28-37.
A losing bonus point would have seen Clermont clinch top spot in Pool 2 on points difference over Exeter Chiefs. However rather than kick a straightforward penalty, Parra went quick and the chance was lost when Noa Nakaitaci was held up over the try line.
In a group where all four sides could technically qualify, it appeared as though Clermont were in the driving seat after going into a 14-0 lead through Jonathan Davies and Nakaitaci tries.
However, UBB showed tremendous spirit to come back into the contest and eventually be in front by the interval.
Berend Botha and Sébastien Taofifenua went over and Baptiste Serin kicked a penalty as the visitors moved 17-14 ahead.
Serin added a second three-pointer but Auvergne hit back via Damien Chouly and Paul Jedrasiak tries.
That looked to have finished off the visitors until Paulin Riva and Peter Saili went over and Pierre Bernard scored a final penalty.
It left the home side on 15 points while the visitors ended on 16 in Pool 2, along with the Exeter Chiefs and the Ospreys, but the West Country outfit's better head-to-head record meant the English team qualified.
Before the match, the hosts were still favourites to make it through to the quarter-finals, despite an intermittent European campaign.
To do so they ideally needed a bonus-point victory and two tries in the first four minutes suggested that it was going to be a comfortable afternoon for Clermont.
Firstly, Davies crossed the whitewash following good work by Nakaitaci before the wing was rewarded for his industry with a score of his own.
It was a scintillating opening but one they could not build upon and UBB's response was excellent.
They also needed a four-try win and the away side played without fear. UBB halved the deficit from close-range through Botha and the gargantuan Taofifenua levelled matters with another barrelling run.
Serin then took Bordeaux into the lead at the break from the tee and added another three points early in the second period.
That made the score 20-14 in the visitors' favour before there was another turning point in the contest when Sekope Kepu was sin-binned.
While the prop was off the field, Auvergne scored twice. Aurélien Rougerie was the inspiration as he broke through the defensive line before being hauled down just short.
The ball was shifted to the right and Chouly powered over for a crucial try. Jedrasiak then touched down to move the home team eight points clear.
Once again, Clermont looked to be in the ascendency but a yellow card for Julien Bardy brought UBB back into the contest.
It proved vital as Riva and Saili went over in quick succession before Bernard's penalty sealed an incredible triumph as Clermont failed to score the necessary points to finish within seven in the final moments.
Tries: Davies, Nakaitaci, Chouly, Jedrasiak
Cons: Parra 4
Yellow Card: Bardy
Tries: Botha, Taofifeuna, Riva, Saili
Cons: Beauxis 2, Bernard 2
Pen: Serin 2, Bernard
Yellow Card: Kepu
Clermont: 15 Scott Spedding, 14 Hosea Gear, 13 Jonathan Davies, 12 Wesley Fofana, 11 Noa Nakaitaci, 10 Camille Lopez, 9 Morgan Parra, 8 Fritz Lee, 7 Alexandre Japandry, 6 Damien Chouly, 5 Sébastien Vahaamahina, 4 Paul Jedrasiak, 3 Daniel Kotze, 2 John Ulugia, 1 Thomas Domingo
Replacements: 16 Benjamin Kayser, 17 Raphael Chaume, 18 Mickael Simutoga, 19 Loic Jacquet, 20 Julien Bardy, 21 Ludovic Radosavljevic, 22 Pato Fernandez, 23 Aurélien Rougerie
UBB: 15 Darly Domvo, 14 Metuisela Talebula, 13 Jean-Baptiste Dubié, 12 Romain Lonca, 11 Sofiane Guitoune, 10 Lionel Beauxis, 9 Baptiste Serin, 8 Matthew Clarkin, 7 Peter Saili, 6 Luke Braid, 5 Adam Jaulhac, 4 Berend Botha, 3 Sekope Kepu, 2 Clement Maynadier, 1 Sébastien Taofifenua
Replacements: 16 Ole Avei, 17 Steven Kitshoff, 18 Jean-Baptiste Poux, 19 Cyril Cazeaux, 20 Marco Tauleigne, 21 Heini Adams, 22 Pierre Bernard, 23 Paulin Riva
Referee: JP Doyle (England)
Assistant Referees: Matthew Carley (England), Paul Dix (England)
TMO: Graham Hughes (England)