Liverpool came back from a goal down to defeat Turkish side Tranzonspor to make sure of a place in the group stage of football's Europa League on Thursday.
The German trio of Bayer Leverkusen, Borussia Dortmund and VfB Stuttgart also went through, while Villareal, PSV Eindhoven, Paris St Germain, Sporting Lisbon and and Besiktas were among other successful sides, DPA reported.
Liverpool found themselves behind to a fifth minute goal from Colombian Teofilo Gutierrez to put the sides level on aggregate in the qualifying play-off.
But Giray Kucar put the ball into his own net from a Glen Johnson cross in the 84th minute and Dirk Kuyt grabbed the winner two minutes from time.
"I thought we were a bit unlucky with their early goal, but we got over it and played quite well and we should have had the game sewn up long before we did," said Liverpool manager Roy Hodgson.
"They are a very good team, they don't lose at home and we beat them at home, so it's a very good result."
Sporting Lisbon overturned a 2-0 home defeat to Brondby by beating the Danish side 3-0 with a dramatic injury-time decider from Yannick Djala following goals from Evaldo and Nuno Coelho.
Dutch side PSV Eindhoven cancelled out a 1-0 first leg deficit to Sibir Novosibirsk with a 5-0 rout at home.
VfB Stuttgart recovered after going 2-0 down at home to Slovan Bratislava to pull level at 2-2 for a 3-2 aggregate win.
Martin Dobrotka in the ninth minute and Jakub Sylvestr in the 53d had put Slovan in a good position but the game changed after Martin Breznanik was sent off two minutes later for a second yellow card.
Timo Gebhart pulled a goal back a minute later and Christian Gentner struck the crucial equalizer with a long-range effort in the 64th.
A stoppage-time goal from Lucas Barrios gave Borussia Dortmund a 1-0 win at Qarabag Agdam to seal their place in the group stage.
The victory in Azerbaijan completed a 5-0 aggregate win for the Bundesliga side. Leverkusen meanwhile were 3-1 winners at Ukrainians Tavriya Simferopol for a 6-1 aggregate.
Spain's Villareal followed up last week's 5-0 thrashing of Dnepr Mogilev with a 2-1 win in Belarus, Marco Rubin scoring a last-minute winner after Nilmar had cancelled out an opener from Vladimir Yurchenko.
Brugge were 3-2 winners at Dinamo Minsk to follow up their 2-1 win at home in the first leg.
Alkmaar went through 3-2 on aggregate despite a 2-1 defeat at Kazakh side Aktobe, while BATE came away from Portugal's Maritimo with a 2-1 win for a 5-1 aggregate.
Paris St Germain lost 4-3 at Maccabi Tel Aviv but it proved enough for a 5-4 aggregate win. AEK Athens were held 1-1 by Dundee United but go through 2-1 on aggregate.
Besiktas belted HJK Helsinki 4-0 to follow up a 2-0 first-leg victory in Istanbul last week.