Goals from Jose Antonio Reyes and Kevin Gameiro either side of half-time set Sevilla on their way to a 2-1 second-leg win in Spain and a 4-3 aggregate victory.
Maribor pulled a goal back through Dare Vrsic in stoppage time to briefly set the nerves jangling at the Ramon Sanchez Pizjuan, but they could not find an equaliser to leave Sevilla with a derby date against Betis next month.
Another late Vrsic goal in the first leg earned Maribor a 2-2 draw but 2006 and 2007 UEFA Cup winners Sevilla would always have fancied their chances of going through in front of their own fans.
They laid siege to Slovenian champions' goal early on and visiting goalkeeper Jasmin Handanovic needed to produce heroics to deny Gameiro and Reyes in the opening seven minutes before Ivan Rakitic, Piotr Trochowski, Gameiro and Alberto Moreno all tried their luck without success.
Somehow though the Maribor goal survived and it looked like they would go into the break still on level terms until Reyes fortuitously gave Sevilla the lead in the 42nd minute.
The former Real Madrid winger charged down Handanovic's attempted clearance on the edge of the box and saw the ball rebound into the net.
The hosts then doubled their lead, and seemingly put the tie to bed, just before the hour when Gameiro turned in Vicente Iborra's flick.
Sevilla continued to push for more goals and Rakitic tried - and failed - three times to beat Handanovic before Maribor attempted a late fightback.
Vrsic saw a rare effort saved by Javi Varas with eight minutes to go but the Slovenia international did manage to find the back of the net after the game had entered stoppage time, finishing off Martin Milec's cross at the far post.
That was a scare for Sevilla but it would be no more than that as they held out for the little time that remained to earn their shot at Betis.