Peter Crouch scored his fourth Champions League goal of the season to secure a priceless victory for Liverpool in Bordeaux and keep the Reds top of Group C .
Crouch had missed two decent first-half chances before firing home a fine header from Craig Bellamy's corner.
Liverpool were without Steven Gerrard with a hamstring injury and boss Rafael Benitez decided not to risk Mohamed Sissoko and Dirk Kuyt from the start.
Midfielder Sissoko and striker Kuyt, who travelled to France with slim hopes of starting, were on the bench along with young reserve Lee Peltier.
It left Liverpool with Luis Garcia and Mark Gonzalez on the flanks, Boudewijn Zenden in central midfield and the only fit strikers in Craig Bellamy and Peter Crouch up front.
The Group C game in the Stade Chaban-Delmas was set to dictate whether Liverpool would have a comfortable ride into the next stage or whether it was going to be hard going right to the final match in Istanbul against Galatasaray.
Liverpool's first away win of the season would make life so much more comfortable for Benitez, whose side is suffering international fatigue, loss of confidence and a seemingly collective failure of senior players to find consistent form.
The apparent slowness in the Bordeaux defence twice gave encouragement to Bellamy in the opening minutes.
The ball did not run for the Wales striker, but he was instantly aware of the potential to get behind Tunisia international David Jemmali.
On seven minutes, a John Arne Riise free-kick was chested into Bellamy's path by Luis Garcia, the striker turning to hit a shot that Ulrich Rame scooped away from Crouch.
But the game soon settled into one of Bordeaux possession and steady progression towards Liverpool's deep back line. One clever push through Riise's legs by Alejandro Alonso created a chance for a driven cross that skipper Jamie Carragher was forced to dive full-length to head away.
On 20 minutes Gonzalez cut in from the left and tried a shot, held by Rame, when he should have been looking for the movement ahead of him. A minute later Franck Jurietti was booked for a foul on the Chile international.
Zenden was booked for a foul on Alonso and Bordeaux's pace quickened as they saw Liverpool prepared to sit and invite them on.
Bellamy saw a flicked header deflected for a corner before, after 35 minutes, Crouch missed a sitter when he cruised in on the right, evading the offside trap, but could only steer Xabi Alonso's long pass wide of the far post.
Gonzalez and Crouch contrived to lose possession deep in their own half and only a fine block by Sami Hyypia saved the day.
After 39 minutes Alonso again provided the ammunition and Crouch got in on the far post for a shot that Rame did well to turn behind.
And when former Sunderland forward Lilian Laslandes was hurt in the centre circle
Rame ran from his goalline to complain and was booked for his troubles.
HT: Bordeaux 0 Liverpool 0
The French side, who had 65% of the opening period possession to underline the problems Liverpool were creating for themselves, were soon on the attack in the second half - Fernando Menegazzo testing Reina with a snapshot a minute after the restart.
Laslandes and Jean-Claude Darcheville - another player who has had time in the English league, this with Nottingham Forest - were beginning to cause growing danger with their movement and pace.
Liverpool started to hit back when Riise's fine crossfield pass found Luis Garcia, and the little Spaniard cut in to force Rame into an important save.
But in the 58th minute Liverpool took the lead, with Crouch planting a firm header from Bellamy's corner past Rame from 10 yards.
Crouch was replaced by Kuyt seven minutes later, while Bordeaux sent on Marouane Chamakh and Julien Faubert for Laslandes and Alejandro Alonso.
Next into the fray for Liverpool was Sissoko in place of Gonzalez, while Bordeaux sent on their Columbia international Edixon Perea for Darcheville.
Bordeaux came close to an equaliser when Chamakh sent a flashing header from Geraldo Wendel's cross inches wide with eight minutes left then Menegazzo saw a low header go wide from Jurietti's ball.
Kuyt was booked for kicking the ball away from a free-kick as Bordeaux kept coming forward.
Stephen Warnock came on for Bellamy with four minutes left and almost grabbed a second when he worked his way clear from Zenden's pass but hit his shot straight at Rame from 12 yards.
Paul Walker, PA Sport
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