Both Ukrainian champions Dynamo Kiev and Norway's Rosenborg Trondheim also put themselves in a strong position to qualify for the group stage with away victories, but Dutch giants Ajax slipped to a 1-0 defeat at home to Slavia Prague.
Liverpool - who have reached the final twice in the last three years, losing last season's final in May to AC Milan - were full value for a 1-0 victory in Toulouse which was clinched with a fine goal by new signing Andriy Voronin two minutes before half-time.
Manager Rafa Benitez made a number of changes to the side that beat Aston Villa on Saturday, with England forward Peter Crouch and Ukrainian striker Voronin - a summer signing from Germany's Bayer Leverkusen - starting up front.
The duo justified their inclusion when Crouch flicked on a Steve Finnan long ball and Voronin controlled the ball with his back to goal before turning and rifling a shot into the top corner from outside the area.
Fellow Premiership side Arsenal earned a 2-0 win at Sparta Prague with Cesc Fabregas on target in the 72nd minute and Alexandr Hleb notching the second in the last minute.
Czech rivals Slavia Prague meanwhile upset Ajax in Amsterdam 1-0 with a 76th penalty converted by David Kalivoda.
Germany's Werder Bremen, attempting to reach the group stage of the competition for a fourth successive season, came from behind to beat Croatian champions Dinamo Zagreb 2-1.
Injury-hit Bremen struggled for long periods to cope with the visitors who took the lead in first-half stoppage time when striker Bosko Balaban got on the end of a low cross from Mario Mandzukic.
However half-time substitute Hugo Almeida immediately made an impact by equalizing 38 seconds after the break and another sub, Daniel Jensen, struck a 30-minute piledriver with five minutes remaining to earn Bremen a win.
Spanish side Sevilla overcame visiting AEK Athens with second-half goals by Brazilian Luis Fabiano and French strike partner Frederic Kanoute. In Moscow, a powerful header from Paul Hartley gave Celtic a 21st-minute lead against Spartak but the home side got back on level terms through Roman Pavlyuchenko 20 minutes later.
Two goals from Yssouf Kone helped Norway's Rosenborg Trondheim to a 3-0 win at Finland outfit Tampere United and have virtually booked their place in the group stage.
Romanians Steaua Bucharest conceded a last-minute goal to settle for a 2-2 draw at Belarussian hopefuls BATE Borisov.
BATE had already made Belarussian history by becoming the country's first side to progress through two qualifying rounds of the Champions League.
They took the lead in the 43rd minute through Artem Radkov before Dorin Goian in the 58th and Nicloae Dica in the 84th put Gheorge Hagi-coached Steaua ahead, only for the home side to equalize in the last minute through Gennadi Bliznyuk.
Ukraine's Dynamo Kiev were 1-0 winners at FK Sarajevo thanks to a 12th-minute goal from Maksim Shatshikh but fellow Ukrainians Shaktar Donetsk slipped 1-0 at Austria's Red Bull Salzburg for whom Alexander Zickler converted a 10th-minute penalty.
A goal from Alex in the 32nd minute gave Fenerbahce a 1-0 home win over Anderlecht, while fellow Turkish side Besiktas earned a 1-1 draw away to FC Zurich. A 4th-minute goal from Argentinian Matias Delgado was cancelled oput in the last minute by Zurich Alexander Alphonse.
Return-leg matches are being played on August 28 and 29, with the winners going into the draw for the 32-team main group stage.