Michael Ciani popped up with the only goal of the game on the stroke of the interval as the Greek side gave themselves a mountain to climb in the second leg on March 17.
The winner was not without a whiff of controversy, however, coming as it did from a controversial free-kick awarded by referee Howard Webb, but that will be of little concern for Bordeaux coach Laurent Blanc who saw his side maintain their unbeaten record in this season's competition.
Olof Mellberg almost opened the scoring for Olympiacos after just four minutes, the defender connecting well with Jesus Datolo's free-kick but unlucky to see his header sail the wrong side of the upright.
Neither did enough to claim the upper hand in the early exchanges but Antonis Nikopolidis' palms were stung after 25 minutes when some neat Bordeaux approach play saw Fernando fire an effort straight at the home custodian.
A collision between Raul Bravo and Ieroklis Stoltidis gifted Bordeaux a chance to bag the opener after 36 minute but Mellberg was on hand to mop up, flicking the ball clear of danger as Yoann Gourcuff looked to pull the trigger.
Two minutes into stoppage time Webb awarded a harsh free-kick against Lomana Lua Lua - who appeared to win the ball cleanly from Benoit Tremoulinas on the left touchline.
Lua Lua was frustrated by the decision, but frustration gave way to anger moments later when Gourcuff whipped in a wicked delivery and centre-half Ciani timed his run to perfection to nod home from six yards.
In the second half the visitors saw an opening to go two goals clear spurned as Ciani headed over when unmarked from a corner kick.
Wendell screwed a shot wide of the target on 80 minutes as the visitors again looked the most likely to add to the scoring, but 60 seconds later Olympiacos went close.
Olympiacos almost snatched an equaliser at the death when more frantic Bordeaux defending saw Fernando hack clear Stoltidis' header off the line
VINTAGE BORDEAUX IN GREEK CRUISE
