Ulster's Justin Fitzpatrick tackles Arnaud Tchougong of Bourgoin
Ulster (6) 25
Tries: Bowe, Marshall, Trimble
Cons: Humphreys (2)
Pens: Humphreys (2)
Bourgoin (17) 24
Tries: Coux, Denos, Vigneaux, Petrilli
Cons: Parra (2)
Ulster snatched a remarkable first win of a poor Heineken Cup campaign thanks to a late try by Andrew Trimble.
The win looked unlikely as tries from winger Jean Francois Coux, full-back Florian Denos and hooker Remi Vigneaux saw Bourgoin take first-half command.
David Humphreys set up Tommy Bowe for Ulster's first try early in the second half but Augusto Petrilli replied.
Scrum-half Paul Marshall dived in at the corner to reduce the deficit before centre Trimble got the crucial score.
Ulster now have five points but stay bottom of Pool Two with third-placed Bourgoin also out of contention on seven.
It had looked bad for Ulster as their line was crossed by Bourgoin in the first minute with Coux making the left corner.
Two Humphreys penalties gave the home side a brief 6-5 lead.
Bourgoin hit back quickly when Denos put in a grubber kick on Ulster's 22-metre line and dived on the ball as it rolled over the line.
Then in first-half stoppage-time Julien Frier intercepted a Marshall pass off the deck and took the ball just short of the try line for Vigneaux to score under the posts.
Bowe's try gave Ulster something to chase before Marshall's try and Trimble's heroics secured the win.
Ulster: B Cunningham; T Bowe, A Trimble, P Wallace, S Danielli; D Humphreys, P Marshall; J Fitzpatrick, N Brady, D Fitzpatrick, c Del Fava, capt, R Caldwell, M McCullough, N Best, G Webb.
Replacements: B Young, S Philpott, J Harrison, D Pollock, M McCrea, I Boss, N O'Connor.
Bourgoin: Denos, Nicolas, David, Carmona, Caux, M Forest, Petrilli, Jooste, Frier, Wyatt, Pierre (capt), Sourgens, Vigneaux, Tchougong
Replacements: Genevois, Cardinali, Rennie, Monzeglio, Viazzo, A Forest, Romanet