New Liverpool boss Juergen Klopp made it three wins from his last three matches with a 1-0 success at Rubin Kazan in Russia that left them second in Group B, two points behind Swiss club Sion on Thursday.
Jordon Ibe netted his first goal for Liverpool, latching on to a neat pass from Roberto Firmino to power into the penalty area and fire right-footed into the bottom corner.
James Milner and Ibe had shots saved before the visitors held off late pressure.
Second-placed Liverpool are three ahead of Bordeaux, who visit Anfield on 26 November.
The Reds will qualify for the knockout stages if they win that match, with their last game a trip to Switzerland to face Sion.
It was a good night for Premier League clubs as Tottenham Hotspur beat Anderlecht 2-1 to go top of Group J thanks to a stunning 87th-minute winner from Mousa Dembele.
After Anderlecht's Imoh Ezekiel had cancelled out Harry Kane's first-half opener in the 72nd minute, Dembele fired home an unstoppable left-foot shot from outside the area.
Borussia Dortmund and Napoli were the headline acts to qualify for the Europa League knockout stage as both sides plundered a glut of goals in Thursday's group matches.
Dortmund brushed aside Azerbaijani outfit FK Qabala 4-0 in Germany while Napoli went one better with a 5-0 home thrashing of Danish side Midtjylland.
There were some superb finishes to savour as Dortmund eased past Qabala with Germany forward Marco Reus scoring first with an unstoppable low drive after 28 minutes to ensure the Germans had found the net in each of their last 31 competitive games.
Pierre-Emerick Aubameyang doubled the lead with a left-foot effort before halftime and a Sergei Zenjov own goal made it 3-0.
Henrikh Mkhitaryan rounded off the scoring with a shot that thundered into the net off the bar with 20 minutes remaining, leaving Dortmund top of Group C with 10 points.
Napoli waltzed into the knockout rounds and equalled their record European victory with goals from Omar El Kaddouri, a Manolo Gabbiadini double, Christian Maggio and Jose Callejon.
The Italians are now unbeaten in 14 matches across all competitions and sit top of Group D with an unblemished 12 points from their four games.
Mohamed Elyounoussi and the 40-year-old Daniel Hestad were on target for Norwegian champions Molde as they extended their Group A lead and secured their spot in knockout stage.
There were also celebrations for Rapid Vienna who scored a goal in each half through Philipp Schobesberger to beat Plzen and maintain their 100 percent record in Group E.
Braga, Sion, Schalke 04 and Lokomotiv Moscow, however, will have to wait after missing out on the chance of moving forward with two group matches to spare.
Sion had the chance to secure an early spot in the last 32 with a win over Girondins Bordeaux, but needed a 94th-minute own goal from Clement Chantome to snatch a 1-1 draw.
Braga were also denied an early qualification party as they suffered their first defeat in 10 games and lost their 100 percent record in Group F after a 1-0 defeat at Olympique de Marseille with Georges-Kevin N'Koudou scoring in the 39th.
Molde beat former European champions Celtic 2-1 away and Rapid Vienna, who won by the same score at Viktoria Plzen also moved to the last 32.
Locomotive Moscow and Schalke needed wins in their games against Besiktas and Sparta Prague respectively to book spots in the next round but both games ended in 1-1 draws.
There were high-scoring wins for Group L leaders Athletic Bilbao, who beat Partizan Belgrade 5-1, and Augsburg, who eased past AZ Alkmaar 4-1.
Raul Bobadilla grabbed a hat-trick for Augsburg, while Bilbao's Inaki Williams netted a double for the second time in five days following Sunday's La Liga brace against Real Betis.
Albanian side Skenderbeu pulled off a surprise 3-0 home win in Group H over Sporting Lisbon, whose cause was not helped by the sending off of goalkeeper Rui Patricio after 17 minutes.
Fiorentina's Josip Ilicic scored twice in a 2-0 win at Lech Poznan in Group I while Roberto Soldado converted a penalty for Villarreal and then saw his shot deflected home for an own goal by Sergei Politevich in a 2-1 win at Dinamo Minsk in Group E.
