Galatasaray were sent crashing out of Champions League qualification after Young Boys' 1-0 away win secured a 2-0 aggregate victory on Tuesday.
Carrying over a slender advantage from the first leg in Switzerland, Young Boys confirmed their passage to the new-look 36-team competition with the play-off success.
Alan Virginius scored the only goal in the 87th minute before Galatasaray goalkeeper Fernando Muslera was sent off for kicking out at the Young Boys substitute as he celebrated.
RB Salzburg are also set for their sixth straight appearance in Europe's top club competition after a 1-1 draw at home to Dynamo Kyiv wrapped up the tie 3-1 on aggregate.
Adam Daghim struck after just 12 minutes for the hosts before Vladyslav Vanat equalised for Kyiv, who were unable to overturn a 2-0 deficit from their first leg at home.
Sparta Prague were the other side to make it through Tuesday's qualifying, thanks to a 2-0 win over Swedish side Malmo that completed a 4-0 triumph on aggregate for the Czech champions.
Anders Christiansen missed a first-half penalty for Malmo before a late spot-kick from Lukas Haraslin and a goal for Albion Rrahmani sealed progression.
Wednesday will see four more sides fight for a place in the Champions League group stage.