Gavin Henson scored the only try of the game with the boot of James Hook bringing 17 points as the French visitors were able to get a bonus point thanks to five penalty kicks of their own.
The Ospreys got off to the perfect start when James Hook landed an opening penalty from in front of the posts after just three minutes; Hook himself had been caught in possession but the Bourgoin pack went over the top.
Bourgoin squandered a chance to hit back from the kick off when what should have been a scoring pass to right wing Matthieu Nicolas went astray. The Welsh team had to weather a storm on their own line but were able to clear.
After 18 minutes the Ospreys stretched their lead, again it was a Hook penalty after the French team had gone over the top in a ruck. This time the kick was from wider out, but the result was the same.
After 25 minutes there was a return to familiar territory for former Wales lock Chris Wyatt, who came on as a replacement for Bourgoin captain Julien Pierre.
Then the Ospreys scored their first try of the match through centre Gavin Henson luring out on the wing to score in front of new Wales Coach Warren Gatland. He was given the scoring pass by Shane Williams after interpassing by Justin Marshall and Lee Byrne had made 50 yards and created the opportunity. Hook added the conversion.
The home team then lost captain Filo Tiatia for 10 minutes for a high tackle on visiting outside half Benjamin Boyet. It also brought a penalty from in front of the posts, converted by replacement Sebastien Laloo.
Although they were down to 14 men, the Ospreys replied immediately when a line-out barge gave Hook another penalty shot, which he slotted from 35 yards.
The final score of the first half was a second Bourgoin penalty when prop Adam Jones went over the top. Laloo landed the 45 yard penalty, for his side to trail 16-6 at the break.
The Ospreys lead was cut further at the start of the second half when straying offside brought a straightforward penalty for Boyet as Tiatia returned to bring the home side back up to full strength.
Hook restored the 10 point lead with another penalty, the Ospreys had run one kickable penalty going for the try but then went for goal after a deliberate knock on by the visitors broke up that attack.
A Bourgoin attack in which Wyatt was prominent gave a chance to left wing Jean-Francois Coux. He was bundled into touch over the line, but it went to the television match official to decide whether he had grounded the ball first. The result was a drop out 22.
Hook missed a long range chance to extend the lead further when his penalty kick from just under 50 yards out dropped short under the posts. There followed an exchange of penalty kicks, first Boyet from 30 yards and then Hook from a similar distance to take the score to 22-12 with just over a quarter of an hour to go.
The Ospreys fell offside from a Henson up and under which only went a few yards forward, but Boyet’s penalty attempt fell a few feet short. However, he was just finding his range as he slotted another effort from a couple of yards closer just a few minutes later to bring his team within range for a bonus point, keeping alive hopes of a victory.
The Ospreys, though, were able to hold out and finished on the attack to seal the victory in their opening group game.
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