A dramatic 59th-minute winner from Franck Dja Djedje gave the Ukrainians the win they needed in Holland to progress at PSV's expense in Group B.
PSV knew a draw would be good enough to advance but they were sunk by Dja Djedje's winner, despite the visitors being reduced to 10 men three minutes from time when Sito Rieira was sent off.
Bulgarians Ludgorets had already been crowned group winners and they completed their campaign with a 2-1 win at Dinamo Zagreb, bouncing back from behind with goals from Duje Cop and Roman Bezjak.
Spanish giants Valencia wrapped up a strong group stage campaign to ease into the last 32 with a 1-1 draw against Kuban Krasnodar in the Mestalla.
Paco Alcacer put the home side in front in the 67th minute before the Russians rallied with an 84th-minute equaliser through Lorenzo Melgarejo. Valencia's Victor Ruiz was sent off in injury time.
The point did not prove enough for Kuban as Premier League Swansea clung on to the second qualifying place in Group A despite a 1-0 defeat in St Gallen, for whom Marco Mathys scored the only goal 10 minutes from time.
Salzburg's 3-0 win over Esbjerg ensured they finished Group C with their 100 per cent record intact, two goals from Sadio Mane and one from Kevin Kampl giving them victory.
Esbjerg were already assured of second place so Elfsborg's 3-1 win at Standard Liege was irrelevant. Lasse Nilsson's double and a third from Mikkel Beckmann ensured a consolation win for the Swedes.
FA Cup winners Wigan waved farewell to European competition as Maribor beat them 2-1 in Slovenia to ensure the runners-up spot in Group D.
Jordi Gomez's penalty put Wigan ahead on 41 minutes but Chris McCann was sent off one minute later and Dejan Mezga equalised from the spot. Zeljko Filipovic's 59th-minute strike won it for Maribor.
Group winners Rubin Kazan wrapped up their group campaign with a 2-0 win over Zulte Waregem in Belgium, Bibras Natcho and Jose Salomon Rondon grabbing their goals.
Fiorentina sealed Group E with a 2-1 win over Dnipro Dnipropetrovsk, goals from Joaquin and Juan Cuadrado cancelling out Yevgeny Konoplyanka's opener. Group whipping boys Pandurii and Pacos de Ferreira drew 0-0 in Romania.
Goals from Stephane Schrock and Constant Djakpa gave Group F winners Eintracht Frankfurt a 2-0 win over APOEL, while Maccabi Tel Aviv made sure of second place with Eran Zahavi's late penalty giving them a 1-0 win over Bordeaux in Israel.
Sevilla sealed top spot in Group H with a 2-0 win in Freiburg, Vicente Iborra and Raul Rusescu scoring the goals which eliminated the German side who had started the night in second place.
Slovan Liberec's 2-1 win in Estoril was enough to send the Czechs through at Freiburg's expense, Josef Sural and Michael Rabusic getting their goals before Junior Seba's late consolation for the hosts.
Lyon duly wrapped up Group I but only after coming from behind to beat Vitoria Guimaraes 2-1 in Portugal.
Antonio Tomane put the hosts in front but Bafetimbi Gomis equalised from the spot after Pedro Correia was sent off on 62 minutes, and Jordan Ferri hit the winner three minutes later.
La Liga strugglers Real Betis were hardly impressive in a goalless home draw with Rijeka but it was enough to ensure they progressed.
Dynamo Kiev booked their place in the knockout stages with a 3-1 win over Rapid Vienna in Ukraine. Terrence Boyd gave the Austrians a shock lead but strikes from Jeremain Lens, Oleg Gusev and Miguel Veloso sent the hosts through.
Belgians Genk had already been confirmed as Group G winners but they wrapped up their group campaign with Jelle Vossen hitting the only goal in a 1-0 win at Thun.
Trabzonspor turned in a gutsy defensive performance to claim the point they needed against Lazio in the Olympic Stadium in Rome, their goalless draw ensuring the Turks pipped the Italians to top spot in Group J.
In the group's other game, Legia Warsaw avoided the indignity of finishing the campaign pointless and goalless as goals from Tomas Jodlowiec and Tomasz Brzyski gave them a 2-0 win at Apollon.
Roberto Soldado scored a hat-trick as Group K winners Tottenham eased past fellow qualifiers Anzhi Makhachkala 4-1 at White Hart Lane.
Lewis Holtby scored the other goal for Spurs after Ewerton had briefly reduced the deficit for the Russian side in the 44th minute.
Also in Group K, Sheriff rounded off their involvement with their first win, beating Tromso 2-0 with goals from Cadu and Ismail Isa.
Stelios Pozoglou's last-minute strike was not enough for PAOK to snatch top spot in Group L from AZ, for whom a 2-2 draw proved enough to progress as group winners.
Thomas Lam's 31st-minute goal put the Dutch side in front before Lucas equalised from the spot. Donny Gorter also converted a penalty to give AZ the lead before Pozoglou's late effort.
Maccabi Haifa came from behind to beat Shakhter Karagandy 2-1 in Israel. Roger Canas gave the Kazakhs the lead but Shoval Gozlan and Shimon Abuhazira turned the game around.