Andriy Voronin scored his first goal in competition for Liverpool as the five-times European champions made an important step towards the Champions League group stage with a 1-0 victory at Toulouse on Wednesday.
The Ukraine striker, who joined the Merseyside as a free agent from Bayer Leverkusen during the close season, struck two minutes from the interval with a clinical 25-metre drive.
The second leg will be played at Anfield in a fortnight's time.
Liverpool, who won their Premier League opener 2-1 at Aston Villa last weekend, started the game with Spain striker Fernando Torres on the bench.
The Reds were the first in action in scorching heat, with a Steven Gerrard free-kick shaving Nicolas Douchez's left post in the third minute.
Toulouse, however, were no pushovers, putting the pressure on the Liverpool defence through midfielder Achille Emana and forward Bryan Bergougnoux.
But Voronin, one of the three Liverpool new signings to start the game with Ryan Babel and Yossi Benayoun, opened the scoring shortly before halftime.
The Ukraine striker received a long ball from Peter Crouch before firing it into Douchez's left top corner.
The hosts came close to draw level on the stroke of halftime when Achille Emana's overhead kick went just wide.
Toulouse coach Elie Baup strengthened his midfield just after the break by bringing in Fode Mansare in place of Bergougnoux.
Benitez replaced Benayoun by John Arne Riise and Gerrard by Momo Sissoko after Emana stepped on the Liverpool skipper's foot.
Sweden striker Johan Elmander, who gave Toulouse a 1-0 win in Ligue 1 over six-times French champions Olympique Lyon last weekend, forced Pepe Reina to a superb save shortly after the hour-mark.
The Reds, who played the last two Champions League's finals, winning one and losing the other, held on after Voronin made way for Torres 12 minutes from time.