Bourgoin pulled off an extrordinary 32-30 win at London Irish on Thursday to reach the semi-finals of the European Challenge Cup.
Delon Armitage missed a late chance to force extra-time, after a bizarre finale including a drop goal from England lock Nick Kennedy.
The French side looked assured of a semi-final place when replacement Matthieu Nicolas' try helped put them 10 points ahead with time almost up.
But Kennedy kicked a drop goal before flanker Steffon Armitage went over in the corner in a fabulous last five minutes.
But Armitage's brother Delon, who kicked 17 points, was off target with the conversion attempt to leave the Guinness Premiership as Irish's sole route for Heineken Cup qualification next season.
Having scored 212 points in their three Challenge Cup group matches at the Madejski, Irish's backline found life much harder going against Bourgoin.
They fell behind on five minutes after centre Charlie Gower was penalised for holding on and French international scrum-half Morgan Parra slotted a simple three points in front of the posts.
Armitage drew Irish level after a Bourgoin offside after 10 minutes and was then involved in a scintillating break with wing Sailosi Tagicakibau that was only halted by Benjamin Boyet's tackle.
The full-back notched another penalty soon after but after missing one attempt earlier Boyet made it 6-6 with a drop goal.
Another Bourgoin offence at the ruck allowed Delon Armitage to put the home side ahead on the half-hour mark, only for prop Tonga Lea'aetoa's high tackle giving Parra the chance to establish parity.
But right on the stroke of half-time Irish constructed the best move of the match when Peter Hewat's kick to the corner just bounced over Seilala Mapusua's head.
There was a penalty coming though and Delon Armitage maintained his perfect record with the boot to put his side 12-9 ahead at the break.
Any half-time message from coach Toby Booth was quickly forgotten by his side as they conceded the game's first try almost straight from kick-off.
Bourgoin took a quick lineout and good hands from Yann Labrit, Bogdan Leonte and Jean-Phillipe Genevois helped put full-back Anthony Forest away. Boyet added the extras.
Delon Armitage should have brought his side to within one point but missed a straightforward penalty just outside the Bourgoin 22 after 50 minutes.
But the hosts did finally make the breakthrough five minutes later.
Topsy Ojo's searing break laid the platform and after both Gower and Hewat had been held up just short, Mapusua barged over from close range. Delon Armitage converted for a 19-16 advantage.
Yet instead of settling the home nerves, Bourgoin quickly re-established their lead thanks to two further Parra penalties, the second of which was for a high tackle by replacement Chris Hala'Ufia which resulted in a yellow card.
Some urgency was finally injected into the home side's game and with 10 minutes remaining Delon Armitage's penalty made it 22-22.
Bourgoin hit straight back through Boyet's drop goal and Nicolas picked off Mapusua's ambitious pass to go under the posts.
But there was still time for Kennedy to kick an unlikely drop goal and deep into added time flanker Steffon Armitage's score was given the thumbs up by the television match official only for his brother to push the conversion wide.
For London Irish:
Tries: Mapusua, S.Armitage
Pens: D.Armitage 5
Drop goal: Kennedy
Tries: Forest, Nicolas
Cons: Boyet, Parra
Pens: Parra 4
Drop goals: Boyet 2
London Irish: 15 Delon Armitage, 14 Topsy Ojo, 13 Seilala Mapusua, 12 Craig Gower, 11 Sailosi Tagicakibau, 10 Peter Hewat, 9 Peter Richards, 8 Richard Thorpe, 7 Steffon Armitage, 6 Kieran Roche, 5 James Hudson, 4 Nick Kennedy (capt), 3 Tonga Lea'aetoa, 2 Danie Coetzee, 1 Dan Murphy,
Replacements: 16 Clarke Dermody, 17 David Paice, 18 Gary Johnson, 19 Chris Hala'Ufia, 20 Jonathon Fisher, 21 Paul Hodgson, 22 Adam Thompstone.
Bourgoin: 15 Anthony Forest, 14 Rudi Coetzee, 13 David Janin, 12 Yann David, 11 Jean-Baptiste Coux, 10 Benjamin Boyet, 9 Morgan Parra, 8 Yann Labrit, 7 Wessel Jooste (capt), 6 Julien Frier, 5 Camille Levast, 4 Coenie Basson, 3 Karena Wihongi, 2 Jean-Philippe Genevois, 1 Arnaud Tchougong.
Replacements: 16 Pablo Cardinali, 17 Wessel Roux, 18 Thomas Genevois, 19 Bogdan Leonte, 20 Mickael Forest, 21 Matias Viazzo, 22 Florian Denos
Referee: Peter Allan (Scotland)
Assessor: JoÃ«l DumÃ© (France)
Touch judges: Andy Macpherson (Scotland), Alan Forrest (Scotland)
Television match official: John Burtenshaw (England), Iain Ramage (Scotland)