Bundesliga outfit Mainz let slip a 1-0 first-leg lead as they succumbed to a 3-1 defeat at Greek side Asteras Tripolis in the return fixture to suffer the ignominy of an early exit.
Kasper Hjulmand's men appeared set to go through after Koo Ja-cheol cancelled out Pablo de Blasis' opener.
However, a second-half double from striker Pablo Mazza settled the tie in the hosts' favour.
Hull, meanwhile, were grateful to a late goal from substitute Sone Aluko, the forward finding the net 10 minutes from time to give the Premier League side a 2-1 success versus Trencin after a 0-0 draw in their first leg.
Captain Xabi Prieto scored twice as Real Sociedad beat Aberdeen 3-2 in a thrilling game at Pittodrie, earning a 5-2 aggregate win capped by Markel Bergara's injury-time strike.
Celtic, who will feature in the Europa League play-off round following their exit from the Champions League, are the only Scottish side remaining in Europe after St Johnstone went down 3-2 on aggregate to Spartak Trnava, having drawn the second leg 1-1.
PSV progressed in unconvincing manner, the 1978 winners overcoming St Polten 3-2 in Austria to win the tie 4-2.
However, there were no such difficulties for Club Brugge or Torino, who each sailed through in emphatic fashion.
Brugge went through 5-0 on aggregate with a 2-0 success at Brondby, and Torino crushed Brommapojkarna of Sweden 4-0 to win 7-0 across two legs.
Brommapojkarna's Allsvenskan rivals Gothenburg – two-time winners of the UEFA Cup – and AIK were also knocked out, but Elfsborg progressed 5-3 on aggregate despite losing 2-1 to FH.
In-demand Lyon striker Alexandre Lacazette was on target as the French side progressed 6-2 on aggregate by beating Mlada Boleslav 2-1.
Young Boys' 2-0 win at 10-man Ermis secured a 3-0 aggregate success, with the hosts' misery encapsulated by defender Paulinho's red card a minute into the second half.
Dinamo Moscow came from behind to earn a 2-1 victory at Hapoel Ironi Kiryat Shmona, winning the tie 3-2, but Cluj will go no further after a 2-0 home loss to Dinamo Minsk saw them go out 3-0 on aggregate.
There was better fortune for Cluj's Romanian compatriots Petrolul, who qualified by an aggregate score of 5-2 after a 4-1 hammering of Viktoria Plzen.
Both RNK Split and Hajduk Split progressed on a strong night for Croatian teams that also saw Rijeka win 4-0 and 9-1 on aggregate against Vikingur.
Lech Poznan exited the competition after they were held to a goalless home draw by Stjarnan, which sealed a 1-0 aggregate loss. However, Ruch Chorzow went through on away goals with a 2-2 draw at Esbjerg.
Karabukspor qualified in similar fashion with a 1-1 draw at Rosenborg; Krasnodar cruised through against Diosgyor and Shakhtyor eliminated Zulte Waregem.
Elsewhere, Zorya, Astra, Neftci, Zimbru, Omonia Nicosia and Sarajevo all ensured their respective places in the next round.
