The home side were 21-6 ahead with half an hour remaining courtesy of penalty hat-trick scorer Bustos Moyano's conversion of their second try of the match, but Biarritz scored their only try of the contest almost immediately thereafter to begin eventually clawing back to a competitive scoreline.
The result moves Montpellier up one place into third ahead of Toulon, who are in action on Saturday against secured semi-finalists Toulouse.
Toulouse meet Montpellier on the final day of the championship, and their 14th win of the season means beginning their play-offs crusade at home is also a distinct possibility.
Biarritz meanwhile find themselves at risk of dropping out of the Top 14 despite picking up a bonus point.
They need to defeat Stade Francais next week to guarantee survival as they currently find themselves in eighth on 46 points.
In-form Montpellier were defeated finalists last campaign, and have stormed into contention for a second year running with a late burst of 12 wins from 16 which has taken them from 11th after nine matches to the play-offs.