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.
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 the goalkeeper from 12 yards.