Having won the opening leg 2-1 last week - a victory overshadowed by a lengthy delay due to crowd disturbances, which led to both clubs being charged by UEFA and facing a potential suspension from competition in the future - Lyon were beaten by the same scoreline before keeping their cool in a penalty shootout at the Vodafone Arena on Thursday.
Thankfully there was no repeat of the ugly scenes witnessed in France and instead it is captain Gonalons and goalkeeper Lopes who will dominate the headlines after Lyon followed up Monaco's achievements in the Champions League by securing their place in the last four of Europe's secondary competition.
After 12 successful penalties, Lopes saved from Dusko Tosic, only for Christophe Jallet to blaze over. But Lopes saved again from Matej Mitrovic, allowing Gonalons to calmly convert and send Lyon through.
With a top-three finish in Ligue 1 no longer a prospect, the Europa League represents Lyon's only chance of a return to the Champions League, which could prove crucial in their ability to hold on to top scorer Alexandre Lacazette.
After Anderson Talisca had fired Besiktas ahead midway through the first half, Lacazette swiftly restored parity on the night with a sublime 31st goal of the season following a one-two with Gonalons.
Talisca's header had the tie all-square shortly before the hour-mark, while both sides hit the woodwork and spurned gilt-edged opportunities before and during extra time, prior to the penalty drama.
Besiktas made a bright start amid a raucous atmosphere but the home fans were almost silenced in the 14th minute, when Corentin Tolisso broke into the box and controlled Lacazette's pass but could only fire wide.
That miss proved costly as Besiktas forged ahead in the 27th minute.
Oguzhan Ozyakup received a quickly taken corner and fed Talisca, who turned and fired low through a crowd of players into the bottom-left corner from just inside the area.
Besiktas' lead lasted just seven minutes, however, as Lacazette dropped the ball off to Gonalons, whose delightful chipped return was controlled by the striker before a deft lobbed finish stunned the home support.
Lacazette went agonisingly close to doubling his tally four minutes prior to the interval, turning away in despair as his curling effort struck the inside of the right-hand post before rebounding across the face of goal and behind.
Only a fine Lopes save from Cenk Tosun's header prevented Besiktas from pulling level on aggregate in the 56th minute.
Lopes could do little about Talisca's powerful header from Adriano's cross two minutes later, though, the home fans sent into raptures once more.
Lyon almost produced another swift riposte as Lacazette thumped an effort straight at Fabri when played through and the Besiktas keeper - at fault for Lyon's winner last week - produced a superb save after Lucas Tousart's shot deflected heavily off Atiba Hutchinson.
There was a huge let-off for Lyon five minutes from time as Lopes misjudged Ricardo Quaresma's cross, which rebounded back off the post into the path of Ryan Babel, who could only hack a shot wildly into his team-mate Tosun.
In a breathless finish to normal time, Mouctar Diakhaby powered a header straight at Fabri before Lacazette raced clear and smacked a shot against the crossbar in the final minute.
Lyon looked stronger in the first additional period but it was Talisca who ought to have completed his hat-trick, somehow stabbing wide of a gaping goal from eight yards following excellent work from Quaresma.
Either side of the interval, Diakhaby headed wide and Lopes clawed out Tosun's effort before Fabri scrambled across his line to brilliantly deny Tolisso - the last action of note before Lopes and Gonalons broke Besiktas hearts.