Benoit Baby and Fijian Seremaia Burotu scored Biarritz's other tries, Dimitri Yachvili converting three of them and also kicking two penalties.
Zebre's points came from two penalties by outside-half Luciano Orquera.
The win leaves Biarritz second in the group on 14 points, 10 behind leaders Harlequins with one game remaining and needing other results to go their way to qualify, with Zebre bottom and pointless.
- Sports & Recreation
- Dimitri Yachvili