Keeper Aleksandr Gutor was the play-off hero for Dinamo Minsk while Dortmund's Marco Reus scored a hat-trick as the lineup for Friday's draw was confirmed.
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Borussia Dortmund ran out emphatic winners against Odd, Dinamo Minsk prevailed in the only second-leg shoot-out and Ajax rode their luck on a night of UEFA Europa League play-off success for Azerbaijan, who will have two representatives in Friday's group stage draw.
Play-off winners: Bordeaux (FRA), Rubin Kazan (RUS), Qarabağ (AZE), Ajax (NED), Lech Poznań (POL), Krasnodar (RUS), St-Étienne (FRA), Sparta Praha (CZE), PAOK (GRE), Qäbälä (AZE), AZ Alkmaar (NED), Liberec (CZE), Fenerbahçe (TUR), Rosenberg (NOR), Plzeň (CZE), Dortmund (GER), Molde (NOR), Dinamo Minsk (BLR), Athletic Club (ESP), Midtjylland (DEN), Legia Warszawa (POL), Belenenses (POR)
Automatic qualifiers: Schalke 04 (GER), Napoli (ITA), Tottenham Hotspur (ESP), Villarreal (ESP), Olympique de Marseille (FRA), Dnipro Dnipropetrovsk (UKR), Braga (POR), Fiorentina (ITA), Anderlecht (BEL), Liverpool (ENG), Beşiktaş (TUR), Lokomotiv Moskva (RUS), Augsburg (GER), Asteras Tripolis (GRE), Groningen (NED), Sion (SUI)
Transfer from UEFA Champions League play-offs: FC Basel (SUI), Sporting CP (POR), Lazio (ITA), Club Brugge (BEL), Celtic (SCO), APOEL (CYP), AS Monaco (FRA), Rapid Wien (AUT), Partizan (SRB), Skënderbeu (ALB)
Pick of the second-leg action
Qarabağ 3-0 Young Boys (agg 4-0)
Azerbaijani outfit Qarabağ, involved for the first time last season, will return for another stab at the UEFA Europa League group stage after this convincing victory. Brazilians Richard Almeida and Reynaldo were on target in the first half – the former from the spot – increasing the hosts' overall advantage to 3-0. Afran Ismayilov rounded things off just after the hour.
Panathinaikos 2-2 Qäbälä (agg 2-2, Qäbälä win on away goals)
Qäbälä, who began their campaign in the first qualifying round, can look forward to their group stage debut. Qarabağ's domestic rivals made it a night to remember for Azerbaijan with a famous away-goals triumph in Athens, even if they twice surrendered the lead given to them on both occasions by their captain Dodô.
AZ 2-0 Astra Giurgiu (agg 4-3)
AZ were heading out until a late rally accounted for their Romanian visitors, victors over West Ham in the previous round. Centre-back Jop van der Linden gave them the advantage on away goals when he broke the deadlock ten minutes from time, with Robert Mühren adding a second for good measure.
Borussia Dortmund 7-2 Odd (agg 11-5)
Thomas Tuchel's men made it seven wins in as many matches this term with a thumping victory. Marco Reus was the standout performer, registering his third hat-trick in a Dortmund shirt, while Shinji Kagawa struck twice. The Schwarzgelben have scored at least four goals in a game on five occasions this season.
Salzburg 2-0 Dinamo Minsk (agg 2-2, Dinamo Minsk win 3-2 on pens)
Prolific UEFA Europa League marksman Jonathan Soriano levelled the tie on aggregate just before the hour and then converted in the shoot-out as the first three spot kicks were converted. However, Aleksandr Gutor then took centre stage by saving Salzburg's next three penalties, booking the Belarusian team – who claimed a famous matchday six triumph over Fiorentina last year – a place in Friday's draw.
Jablonec 0-0 Ajax (agg 0-1)
Goalkeeper Jasper Cillessen was the hero for Ajax with a 58th-minute penalty save from Ján Greguš. The Eredivisie champions' task became stiffer when Riechedly Bazoer was dismissed 60 seconds later, but Frank de Boer's men held on.