Athletic Club, runners-up last season, and FC Internazionale Milano qualified for the play-offs despite second-leg losses, while there were emphatic wins for Bursaspor and FC Dinamo Moskva.
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FC Internazionale Milano, Olympique de Marseille and Athletic Club all managed to avoid being on the wrong end of an upset as they booked their places in the UEFA Europa League play-offs.
View all of Thursday's 29 third qualifying round second-leg results here.
Inter seemed to have carved out a straightforward path to the play-offs by recording a 3-0 first-leg win at HNK Hajduk Split, and even when Ante Vukušić converted a 23rd-minute penalty in the return at San Siro, few would have predicted problems for the Nerazzurri.
Yet despite having their fair share of efforts on target, the hosts could not find a goal, and Ivan Vuković (58) reduced the Croatian side's overall arrears further. The equaliser was not forthcoming, however, much to the relief of Interistas everywhere.
A 1-1 first-leg draw with Eskişehirspor gave Marseille a slight advantage, but the tie remained very much in the balance. André Ayew's early opener calmed nerves in Istres, André-Pierre Gignac extinguishing them nine minutes before the break. Ayew rounded off the scoring midway through the second period.
Athletic came through their tie against NK Slaven Koprivnica, but by no means unscathed. Last season's runners-up were given a scare as they fell to a surprise 2-1 defeat in Croatia, Iker Muniain's goal separating strikes from Alen Maraš and Mario Gregurina. The Basque side qualified by virtue of their 3-1 first-leg success.
Fabio Borini registered on his home debut for Liverpool FC as the Reds vanquished FC Gomel. The summer signing from AS Roma opened the scoring at Anfield, a goal which was added to by captain Steven Gerrard shortly before the break. Right-back Glen Johnson made it 4-0 on aggregate 18 minutes from time.
Elsewhere, a change in coach brought an upturn in FC Dinamo Moskva's fortunes, the Russian club beating Dundee United FC 5-0 for their first win of the season. Round of 32 participants last term, Legia Warszawa overturned a 2-1 deficit to progress at the expense of SV Ried.
FC Twente, APOEL FC and FC Viktoria Plzeň all made it through, the Czech team with a 5-0 win shaped by a Michal Ďuriš hat-trick. Bursaspor went one better, however, registering the biggest victory of the night, 6-0 at home to Finnish league strugglers KuPS Kuopio.
The play-off draw takes place on Friday in Nyon at 13.30CET, with the third qualifying round winners joining the 14 losing clubs from the same stage of the UEFA Champions League and those teams who begin their European campaigns at this juncture.