Cologne 1-0 Arsenal
(Guirassy pen 62')
Sehrou Guirassy's second half penalty sunk Arsenal and notched up Cologne's second victory in this season's Europa League.
The Frenchman latched onto a return pass and hit the deck under pressure from compatriot Mathieu Debuchy, with replays suggesting minimal contact.
Nevertheless, Guirassy took the penalty himself, sending his shot down the middle to beat David Ospina and send Cologne into second place in the group with one game remaining against Red Star Belgrade.
Arsenal, despite losing in Germany, will qualify for the last 32 as group winners.
Athletic Bilbao 3-2 Hertha Berlin
(Aritz Aduriz pens 35', 66', Williams 82' — Leckie 26', Selke 36')
Hertha Berlin twice squandered the lead to lose 3-2 in a thrilling game in Bilbao — sending the Bundesliga team out of the competition.
Mathew Leckie's bullet header gave Hertha the lead, but the hosts pegged them back immediately through Aritz Aduriz's penalty.
Davie Selke's nodded Hertha ahead again as it looked like the Bundesliga side were on route for a big win on the continent, but another penalty from Aduriz — this time for a handball against Langkamp — drew the Spaniards level again.
Hertha threw it away with eight minutes to play when Williams finished from close range to snatch all three points from Hertha, who can no longer finish in the top two.
Braga 3-1 Hoffenheim
(Goiano 1', Fransergio 81', 90'+3 — Uth 74')
Hoffenheim's debut European campaign is over with a game to spare after losing comprehensively in Portugal.
Braga took the lead after 45 seconds through Marcelo Goiano and the German side struggled to regain their composure.
However, Mark Uth gave them hope with 16 minutes to play, cushioning in Kerem Demirbay's whipped free-kick.
But Fransergio put Braga back in front with nine minutes to play before adding their third in stoppage time.Michael Da Silva