Everton, already eliminated, suffered a humiliating 5-1 defeat at home to the Italian side Atalanta with Danish forward Andreas Cornelius and midfielder Bryan Cristante each claiming a brace.
The Bergamo club progress from Group E along with Olympique Lyon, who crushed Apollon Limassol 4-0.
Seven-times European champions AC Milan crushed Austria Vienna 5-1 after going a goal down. Portuguese forward Andre Silva and Patrick Cutrone each scored twice.
Spain's Villarreal moved into the next round after beating Astana 3-2 to end the Kazakh club's 17-game unbeaten run.
Substitute Cedric Bakambu scored twice after being introduced on the hour to put Villarreal 3-1 up; an 88th-minute Patrick Twumasi goal for the hosts made no difference to the result.
Italian Mario Balotelli scored twice, including a penalty, for Nice as they went through from Group K with a 3-1 victory over Belgium's Zulte Waregem.
European debutants Ostersunds, who now top Group J with ten points, triumphed 2-0 at home to Ukrainian side Zorya Luhansk, taking the lead through an own goal from Dmytro Hrechyshkin in the 40th minute before a long-range effort from Saman Ghoddos secured the win 13 minutes from the end.
Salzburg enjoyed a comfortable 3-0 win over Portugal's Vitoria Guimares thanks to goals from Israeli Moanes Dabour, Andrea Ulmer and South Korean Hwang Hee-chan.
Viktoria Plzen progress after a 2-0 win over Romania's Steaua Bucharest which came after second-half goals from Milan Petrzela and Jan Kopic.
Arsenal were already assured of progress before their trip to Germany but will still be disappointed to have a fallen to the Bundesliga's bottom club.
Sehrou Guirassy's 62nd-minute penalty, after he was brought down by Mathieu Debuchy, was all that separated the two sides although Reiss Nelson and Jack Wilshere both went close to levelling in the final moments but were foiled by Cologne keeper Timo Horn.
Serbian champions Partizan Belgrade progressed with a pulsating 2-1 home win over Young Boys Berne.
Towering Cameroonian striker Leandre Tawamba gave Partizan the lead with a 12th-minute header before Nicolas Ngamaleu equalised with an opportunist goal after the home side failed to clear a corner.
Roared on by a fervent 25,000 home crowd, Partizan snatched the winner early in the second half when striker Ognjen Ozegovic finished off a delightful move.
Real Sociedad progress with Zenit St Petersburg from Group L due to a 1-0 win at Norway's Rosenborg. Mikel Oyarzabal grabbed the winner in the 90th minute.
Portugal's Braga will also be in the last 32 after beating Hoffenheim 3-1. Brazilian midfielder Fransergio scored twice after the break.
(Reporting by Simon Evans)
