Fly-half Arlidge was highly effective with kicks out of hand, but had an off-day in front of the posts, failing with his conversion attempt of Fussell's try.
Yachvili put his side back into the lead with a penalty after 16 minutes. Arlidge replied a minute before the break with his only successful shot at goal, but the Biarritz scrum-half ensured his side were 9-8 ahead at the break with an immediate response.
A late tackle on Wales back-row hopeful Joe Bearman by Pelu Taele-Pvihi gave Arlidge a chance soon after the restart.
But his shot fell short and Biarritz continued their workmanlike approach to set up a drop-goal for centre Damien Traille.
The Dragons were caught napping midway through the half as Magnus Lund and Yachvili combined at the front of a line-out for the scrum-half to claim a soft, but well-worked try.
Yachvili converted and before he added a penalty Dragons full-back Martyn Thomas launched a daring counter-attack that ended in disappointment as he sent out a poor pass.
Yachvili missed a penalty and the hosts gained more hope in the dying minutes when Thomas again threatened, but a lack of support saw the move fail.
Biarritz finished on a high as Yachvili broke away, linked with replacement Laurent Tranier and took the final pass to score. Yachvili also converted to seal victory.
Dragons boss Paul Turner:
"All-in-all it's a disappointing two weeks. We know where we are in Europe now. We're not going to qualify - it's probably mathematically possible is it? I don't know.
"We always said we were going to be competitive, but against sides like these, you've got to be right at the top of your game for both weeks.
"And we were well off last week. We got something together today, but weren't good enough.
"We've got to get back to playing as a team. Individually we were okay today, but our shape wasn't good enough in attack or defence.
"Our kick-chase wasn't good enough and we certainly didn't have anybody of [Dimitri] Yachvili's accuracy and talent on the field."
Man of the match Dimitri Yachvili: "We are very pleased to get this win. We knew it would be difficult coming to Wales and we expected a strong reaction from the Dragons after last week's game.
"It was not easy because the game was delayed from Friday night so that was a disruption, but I thought we played an intelligent game.
"We are in a good position in the Pool but we still have two games to go and we will not stop playing now."
Newport-Gwent Dragons: M Thomas; Brew, Riley, Watkins, Fussell; Arlidge, Lee, McKenzie, S Jones, Bracken, MacDonald, Sidoli, Bearman, G Thomas, Webb. Replacements: Connor for Arlidge (58), Leadbeater for Lee (68), Gustafson for McKenzie (56), Willis for S. Jones (41), Robinson for Bracken (56), Harris for G. Thomas (63), L Evans for Webb (63). Not Used: Gomer-Davies.
Sin Bin: Brew (48).
Biarritz: Brusque; Bolakoro, Hunt, Traille, Erinle; Peyrelongue, Yachvili; Barcella, Terrain, Johnstone, Thion, Taele-Pvihi, Lund, Hall, Vahafolau. Replacements: Mignardi for Hunt (58), Courrent for Peyrelongue (77), Coetzee for Barcella (58), August for Terrain (41), Hughes for Johnstone (67), Moala for Taele-Pvihi (69), Roidot for Vahafolau (52). Not Used: Tranier.
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