With Sevilla having drawn 2-2 at Maribor last week, goals from Jose Antonio Reyes and Kevin Gameiro put them in control with half an hour to play.
Although Dare Vrsic made it 4-3 on aggregate in the final minute, the Slovenian champions could not find the second that would have forced extra-time as Sevilla sealed their passage.
Sevilla will take on a Betis side who were impressive in winning 2-0 in Russia to seal a 3-1 aggregate success over Rubin Kazan.
Nono and Ruben Castro scored the goals and the upcoming derby now gives Betis a chance to salvage something from a dreadful season that currently sees them 11 points adrift of safety at the bottom of La Liga.
Two goals in the final 12 minutes saw Napoli through 3-1 on aggregate at the expense of Swansea City, who for a long period looked on course to secure a shock victory on away goals.
Lorenzo Insigne put the hosts ahead early on, but Jonathan de Guzman's equaliser gave the Welsh outfit hope until strikes from Gonzalo Higuain and Gokhan Inler broke Swansea hearts.
Napoli coach Rafael Benitez - who won the tournament last year with Chelsea - will continue his defence of the title with a tie against Porto, who secured a dramatic away goals victory over Eintracht Frankfurt.
After a 2-2 draw in Portugal, the Germans looked in a strong position when leading 2-0 on the night. Eliaquim Mangala levelled with a brace, but the tie appeared to be settled when Alexander Meier restored Frankfurt's advantage in the 76th minute.
But with four minutes remaining, substitute Nabil Ghilas struck for the visitors to send Frankfurt crashing out.
Another dramatic comeback took place at White Hart Lane as Tottenham scored three goals in 13 second-half minutes to secure a 3-2 aggregate victory over Dnipro, who saw Roman Zozulya sent off for a headbutt on Jan Vertonghen.
Zozulya had given his side a two-goal advantage in the tie early in the second half, but his moment of madness cost his side dear as Christian Eriksen and a brace for Emmanuel Adebayor saw Spurs through.
Tim Sherwood's men will face last year's runners-up Benfica, who ran out 3-0 winners over PAOK to seal a 4-0 aggregate success.
Juventus and Fiorentina will meet in the next round in an all-Italian clash. Juve beat Trabzonspor 2-0 to seal a comfortable 4-0 passage, while Fiorentina's 1-1 draw saw them through 4-2 against Esbjerg.
Ajax suffered their joint-heaviest European aggregate defeat, going down 3-1 to Salzburg on the night and 6-1 over the tie, while Basel's 3-0 win over Maccabi Tel Aviv saw them through after a goalless first leg.
Juninho Quixada's 88th-minute strike saw Ludogorets through at the expense of Lazio, the Bulgarians claiming a 3-3 draw after their 1-0 win in Rome last week.
Ludogorets will face Valencia, whose goalless draw at home to Dynamo Kiev was enough to see them through 2-0 on aggregate.
AZ drew 1-1 with Slovan Liberec, sealing a 2-1 win overall, and will face Anzhi, who beat Genk 2-0 in Belgium after a scoreless first leg.
Elsewhere, Viktoria Plzen earned a surprise 2-1 win in Ukraine to see them overcome Shakhtar Donetsk 3-2. Plzen's reward is a tie with Lyon in the next round, who beat Chornomorets 1-0 after a 0-0 draw last week.
