Bordeaux looked dangerous from the first whistle, and they responded to Olly Barkley's early penalty by scoring the first try through winger Lucas Blanc in the 12th minute.
Barkley hit back with a second penalty for the hosts, but Bordeaux cruised into a comfortable half-time lead thanks to further tries from Mateuisela Talebula, Clement Maynadier and influential number eight Matthew Clarkin.
Seb Jewell spotted a rare gap in the Bordeaux defence to run over and raise hopes of a possible comeback in the early stages of the second half.
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However, the home fans were quickly left disappointed again when Pierre Bernard, who was successful with every conversion attempt at the Kassam Stadium, extended his side's lead with a try of his own in the 51st minute, before Darly Domvo followed his example two minutes later.
Peter Brown reduced the deficit for London Welsh, but the Begles had the final say as Domvo stormed clear for his second try to round off an emphatic win for the visitors.