Ospreys 22 (16)
Centre Gavin Henson claimed an early try for the Ospreys
Pens: Hook 5.
Bourgoin 15 (6)
Pens: Laloo 2, Boyet 3.
Ospreys laboured to victory in their Heineken Cup opener against a Bourgoin side that left the Liberty Stadium with a bonus point that could prove vital.
Two James Hook penalties and Gavin Henson's converted first-half try suggested an easy night for the Welsh.
Bourgoin inched their way back through the boots of first Sebastien Laloo and then Benjamin Boyet.
But the Ospreys had Hook in fine form and the fly-half added three penalties in the second half to keep them ahead.
It took the Ospreys until only the fourth minute to take the lead with Hook's opening penalty, after Bourgoin infringed at a ruck.
But if the home side thought it was going to be an easy night, Bourgoin soon showed their credentials with some fine running rugby - which almost sent Matthieu Nicolas in at the right corner.
Open-side Mark Rennie went close also, but the Ospreys' scramble defence held out.
Despite a break from Marty Holah, in his first Ospreys start, it was mostly Bourgoin in the opening quarter.
It took a half-break from Hook to earn a second penalty from a ruck, which he kicked to extend the home lead to 6-0 in the 19th minute.
A fine inside-pass from Justin Marshall to Lee Byrne set up the Ospreys' try on 27 minutes, finished off when Shane Williams put Henson over.
Bourgoin got on to the scoreboard with a penalty for replacement centre Laloo, as a result of Ospreys captain Filo Tiatia being sin-binned for an illegal tackle.
That was cancelled out by Hook's third penalty in the 38th minute.
But Bourgoin had the final say of the half when Laloo found the target with his second penalty in injury time, although the Ospreys led at the interval 16-6.
After the break, Benjamin Boyet kicked a 43rd-minute penalty for Bourgoin, which was cancelled out three minutes later by Hook's fourth penalty.
The French thought they had their first try when wing Jean-Francois Coux went in at the left corner, but on the intervention of the TMO the score was disallowed.
Hook and Boyet swapped penalties again as the Ospreys led 22-12 after 64 minutes.
But Boyet slotted his third penalty to confirm a bonus point for Bourgoin that the Ospreys could yet rue come the final tally-up at the pool stage.
Ospreys: Lee Byrne; Nikki Walker, Sonny Parker, Gavin Henson, Shane Williams; James Hook, Justin Marshall; Duncan Jones, Huw Bennett, Adam Jones, Ian Gough, Ian Evans, Alun Wyn Jones, Marty Holah, Filo Tiatia (capt).
Replacements: Richard Hibbard for Bennett (80), Paul James for D Jones (71), Hale T-Pole for Gough (75), Ben Lewis, Mike Phillips for Marshall (62), Shaun Connor, Andrew Bishop for Henson (80).
Sin Bin: Tiatia (34).
Bourgoin: Anthony Forest; Matthieu Nicolas, Rudi Coetzee, Yann David, Jean-Francois Coux; Benjamin Boyet, Mickael Forest; Arnaud Tchougong, Benoit Cabello, Olivier Sourgens, Julien Pierre (capt), Bryce Williams, Brice Monzeglio, Mark Rennie, Wessel Jooste.
Replacements: Jean-Phillipe Genevois for Cabello (73), Karena Wihongi for Sourgens (57), Chris Wyatt for Pierre (25), Julien Frier for Monzeglio (46), Morgan Parra for M. Forest (60), Sebastien Laloo for Coetzee (26), David Janin for A. Forest (73).
Referee: David Pearson (England).