Rafael Benitez rotated his squad for the third qualifying round first leg match in south-west France, making six changes from the side which beat Aston Villa on the opening day of the Premier League season.
But despite the fresh legs, Liverpool struggled to create any clear chances during the open stages and their early frustration was summed up when skipper Steven Gerrard skewed high and wide from the edge of the box.
However, they found a breakthrough out of nowhere on 43 minutes when Voronin collected a Peter Crouch flick-on, chested the ball down and drilled the ball into the top corner from 20 yards beyond the despairing dive of Nicolas Douchez.
It was his first goal for the club and was a rare moment of quality in the first half as Benitez's men sweated and toiled in the oppressive heat.
The pedestrian pace continued after the break and the home side struggled to seriously threaten Jose Reina's goal, although Johan Elmander's lively performance kept the Reds' back four occupied.
The Swedish striker evaded the clutches of Sami Hyypia and Jamie Carragher to send in a flicked shot which was held by Reina and later sent an angled header over the top.
Crouch was denied a shot at goal by Douchez as the Reds cruised towards victory, although Gerrard was substituted in the 65th minute after a painful kick on his ankle from Gilles Sirieix - but hopefully it was only a precaution ahead of Sunday's league clash with Chelsea.
Otherwise, Benitez will be satisfied with a controlled performance from his side and will be confident of finishing the job at Anfield a week on Tuesday.