Samuel Adeniran's strike 11 minutes from the end of extra-time completed a stunning comeback for Austria's LASK as they reached the Champions League group stage at Celtic's expenses.
Trailing 3-0 from the first leg, LASK found themselves 4-0 down on aggregate midway through the first half after Callum McGregor struck for the Scottish visitors.
But Nigerian midfielder Moses Usor gave LASK hope just before the break and Celtic started to capitulate.
Goals from Robert Ljubicic, American forward Adeniran and an injury time Florian Flecker effort from close range sent the tie into extra-time.
Adeniran put LASK ahead in the second period of extra-time and could have completed his hat-trick but saw his penalty saved by Finland goalkeeper Viljami Sinisalo.
Having finished second from bottom in the the Europa Conference League league stage last season, LASK will now play in the Champions League group stage for the first time.
Gabon forward Orphe Mbina scored the clinching goal as Azerbaijan's Sabah came from behind against Hapoel Beer-Shiva to book a first ever participation in the Champions League group stage.
Trailing 2-1 to the Israelis from the first leg, Sabah found themselves 1-0 and 2-1 down on their home pitch in Baku.
But Tellur Mutallimov's injury time strike sent the tie to extra-time and goals from Mbina and Rwandan international Joy-Lance Mickels gave Sabah a 5-2 win on the night and 6-4 aggregate success.
Hapoel had Senegal defender Djibril Diop and Israel midfielder Eliel Peretz sent off in extra-time.
Last year's surprise package, Bodo/Glimt, cruised into the group stage for the second year running with a 2-0 victory over 10-man NEC Nijmegen, who had goalkeeper Gonzalo Crettaz dismissed after just three minutes.
Bodo/Glimt reached the last 16 in last season's competition as they registered shock victories over Manchester City, Atletico Madrid and Inter Milan.
Strikes by Fredrik Andre Bjorkan and Sondre Auklend, as well as a Deveron Fonville own goal, gave the Norwegians a 3-0 win on the night and 6-1 aggregate success against their Dutch visitors.