The home side ran in four first half tries to put the game beyond the visitors with Will James, Bill Twelvetrees and George Sharples (2) all touching down, while two Nicolas Sanchez penalties and a late converted score by Gauthier Gibouin ensured the visitors were not embarrassed.
The hosts, keen to use the momentum from their opening win at Mont de Marsan, dominated from the off and took just six minutes to score the first try with James touching down in the corner after he outmuscled Avesini Vasuinubua.
Twelvetrees missed the conversion as he did for their second score six minutes later when the Irishman took advantage of a brilliant kick through by Jimmy Cowan to outrun the Bordeaux backline and touch down.
Sanchez converted two penalties to get his side back into the clash but two Sharples tries, the second made by an excellent Ben Morgan run, put Gloucester well in control at the break, 25-6 ahead.
The second-half was a less frantic affair, but it was the visitors who had the final say as a Gibouin crashed over.
Francois Louw's late try clinched a dramatic 27-22 win for Bath in Pool B against Agen at the Stade Armandie.
Raphael Lagarde's penalty deep into the second half looked to have won it for the home side, but Louw crossed the line in the 79th minute to put Bath back in front and Stephen Donald's conversion added the gloss to the scoreline.
The visitors fell behind in the third minute when Benjamin Petre scored a try for Agen and the accurate Lagarde converted.
Donald and Lagarde exchanged penalties as Agen extended their lead to 10-3, but Michael Claassens scored a crucial try for Bath just before half-time to make it 10-8 to the French side at the interval.
Another Lagarde penalty extended Agen's lead at the start of the second period before Kyle Eastmond crossed for Bath's second try to level the score and Donald's conversion nudged Bath in front for the first time.
Lagarde restored Agen's advantage and, although Donald crossed for Bath in the 54th minute, he missed the conversion and it threatened to cost Bath dear when Lagarde pulled Agen back within a point.
Lagarde's 71st-minute penalty gave the hosts a 22-20 advantage which looked like being enough until Louw's late strike maintained Bath's 100 per cent start to the group.