Hull City are two games away from reaching the Europa League group stage after substitute Sone Aluko struck late on to give them a 2-1 win over AS Trencin in the qualifying third round.
The FA Cup runners-up suffered an early setback at the KC Stadium when Tomas Malec scored for the Slovakians after only 91 seconds, and the Tigers struggled to respond.
Ahmed Elmohamady equalised before the half hour to give Hull a lifeline but, for the next hour, City looked set to exit the competition on away goals.
However, with 10 minutes remaining, super-sub Aluko smashed home from close range to send Hull straight into Friday's draw for the playoffs.
Real Sociedad beat Aberdeen 3-2 at Pittodrie to ensure their progress.
Peter Pawlett and Mark Reynolds scored either side of a first-half Xabi Prieto strike to give Aberdeen a 2-1 lead, but they could not find the further two goals needed to progress.
Sociedad captain Prieto then broke Aberdeen hearts by scoring from the penalty spot with four minutes remaining and Bergara Markel scored moments from the end to give the Basque side victory on the night and a 5-2 aggregate triumph.
Mainz were eliminated by Asteras Tripolis after a 3-1 defeat in Greece.
The Bundesliga side had won the first leg 1-0 but, after going in 1-1 at half-time in the return match, goals from Argentine striker Pablo Mazza in the 68th and 86th minutes saw the hosts progress 3-2 on aggregate.
Torino won 4-0 at home to Brommapojkarna after last week's 3-0 win in Sweden. After Kristinn Jonsson's own goal, Matteo Darmian, Fabio Quagliarella and Josef Martinez added their names to the scoresheet in Turin to ensure a substantial victory.
St Johnstone's quest to reach the group stage ended in failure after they were held to a 1-1 draw against Spartak Trnava.
Stevie May's deflected effort three minutes before half-time handed St Johnstone a lifeline following their 2-1 defeat in Perth but they failed to build on their advantage in the second half.
A blunder from Gary Miller then allowed Martin Mikovic to level with eight minutes left to seal a 1-1 draw for the hosts and a 3-2 aggregate victory.
Lyon went through with a 6-2 aggregate win after beating Mlada Boleslav 2-1 in France with goals from Alexandre Lacazette and Clinton Njie.
PSV Eindhoven won 3-2 at SKN St. Polten to complete a 4-2 aggregate win, with Jurgen Locadia, Memphis Depay and new signing Luuk de Jong on target for the Eredivisie club.