Clermont led by seven points at the interval on Saturday, but were beaten 32-25 as Bordeaux – in their first competitive game under Jacques Brunel – came on strong in the second half.
Both sides scored three tries apiece, with Simon Hickey's five penalties proving decisive for Bordeaux.
Racing 92 came roaring back from 18-3 down to record a 25-21 victory over Castres, Louis Dupichot claiming the match-winning try with just three minutes remaining.