Injury-ravaged Bath claimed a consolation victory in a match between two sides that could not qualify for the Heineken Cup quarter-finals.
HEINEKEN CUP POOL 2
Bourgoin (3) 17
Tries: Janin, Venditti
Cons: Peclier 2
Bath (16) 23
Tries: Lipman, Fidler
Cons: Barkley 2
Pens: Barkley 2
Makeshift winger Michael Lipman caught a looping pass to score the first try after an early exchange of penalties and Bath led 16-3 at half-time.
Rob Fidler was driven over after David Janin had narrowed the margin and David Venditti went over for Bourgoin.
But injury-hit Bath held on with 14 men after David Barnes was yellow-carded.
The win gave Bath second place in Pool 2, ahead of Benetton Treviso but well behind runaway unbeaten leaders Leinster.
Bourgoin finished their campaign with six losses out of six and just two points.
"I'm absolutely delighted with the guys' effort," said Bath coach John Connolly.
"We showed we have strength in depth in our squad, and the pack - without
most of our first-team regulars - dominated the set-pieces in the first half.
"That set us up for a good win."
Bath had only six fit players on the bench - all of them forwards - but opened the scoring in the second minute with an Olly Barkley penalty.
Lipman's try stretched the lead after Alexandre Peclier had levelled the score with a drop goal, and a drop goal from Chris Malone and another Barkley penalty put Bath in control.
Connolly's injury problems continued when number eight Isaac Feaunati had to be replaced at the break.
Fidler's try cancelled out one from Janin, but Venditti's score set up a tense finish.
Bourgoin: Gengenbacher; Esteruizen, Venditti, Coux, Soucaze; Peclier, Campeggia; Castex, Bonet, Pucciariello; Ruiz, Pierre; Freier, Driollet, Raschi.
Remplacements: Milloud, Montagnat, Mazel, Petrilli, Bontinck, Albina, Janin.
Bath: Daniel; Baxter, Crockett, Barkley, Lipman; Malone, Walshe; Loader, Mears, Stevens; Fidler, Hudson; Beattie, Scaysbrook, Lewis.
Replacements: Ward, Barnes, Borthwick, Grewcock, Feaunati, Ovens.