Shakhtar Donetsk, Olympiakos and Fenerbahce all crashed out of the UEFA Champions League in the third qualifying round on Wednesday, while Monaco, Ajax and Celtic got through to the playoff round.
Shakhtar will return to the Europa League this season, having reached the semifinals of the competition last campaign.
Yuya Kubo scored twice in a seven-minute span for Young Boys early in the second half to level the tie 2-2 on aggregate, before both Fred and Yaroslav Rakitskiy misfired in the shootout as the Swiss side went through to the final round of qualifiers.
Valere Germain scored twice as Monaco won 3-1 to overturn a first-leg deficit at Fenerbahce and moved on 4-3 on aggregate.
It only took Germain two minutes to erase Fenerbahce's lead, before a Radamel Falcao penalty in the 18th minute put the Ligue 1 club two goals up on the night.
Emmanuel Emenike's goal for Fener shortly after half-time would have seen the game go to extra time, if not for Valere's second strike of the night in the 66th minute.
Greek champions Olympiakos were undone in Israel as Shir Tzedek's 79th-minute goal was all Hapoel Be'er Sheva needed over the two legs to advance.
Moussa Dembele's first Celtic goal gave the Hoops a dramatic last-gasp 2-1 win over Astana.
The tie had swung towards Brendan Rodgers' side after a 1-1 draw in the first leg, and striker Leigh Griffiths, who levelled in the Astana Arena, scored from the spot on the stroke of half-time before substitute Agim Ibraimi levelled with an opportunist long-range effort.
However, in stoppage time, Dembele slammed in a penalty after he had been tripped by Igor Shitov, who was sent packing by Romanian referee Istvan Kovacs for a second booking, with Dmitri Shomko following him amid the mayhem.
There was also late drama in Thessaloniki as Ajax captain Davy Klaassen scored three minutes from time to provide a 2-1 win over PAOK on the night and put the Dutch giants through 3-2 on aggregate.
After a 1-1 draw in the first leg, PAOK took an early lead through Stefanos Athanasiadis' fourth-minute goal only for Klaasen to level matters again on the stroke of half-time.
With the game seemingly headed to extra time, Klaasen scored from the centre of the box in the 87th minute to stun the hosts.
Belgian side Anderlecht also were eliminated after falling 4-2 on aggregate to FC Rostov.
Christian Noboa and Serdar Azmoun scored either side of half-time as the Russian side, competing in Europe for the first time, won 2-0 on the night.
FC Copenhagen controlled Astra Giurgiu 3-0 to advance 4-1 on aggregate after a first-half brace from Andreas Cornelius either side of Federico Santander's goal.
Nicolae Stanciu scored in either half to help Steaua Bucuresti defeat Sparta Prague 2-0.
The Romanian champs were given a boost in holding on for a 3-1 aggregate win when when Sparta's Jakub Brabec was sent off with a second yellow card in the 51st minute.
Salzburg left it late before completing a 3-0 aggregate win over Partizani, as second-half goals from Jonathan Soriano and Wanderson ensured the Austrian side advanced.
Legia Warsaw also advanced after a goalless draw with Trencin, Nemanja Nikolic's goal from the first leg holding up for the Polish champs.