Returning to Ibrox with a two-goal cushion after their first-leg win in Istanbul, Rangers had already done much of the heavy lifting in this tie.
They weren’t willing to leave anything to chance though, starting on the offensive here and creating a glorious opening when Nicolas Raskin’s cut-back found the unmarked Vaclav Cerny, who couldn’t sort his feet out quickly enough to get an effort on target.
The Gers were forced to survive a scare midway through the half when Talisca tumbled right on the line of the box under a challenge from Jefte, but although there appeared to be contact, referee Espen Eskas booked the Fenerbahce man for simulation.
Cerny was proving to be a constant thorn in the side of the Turkish outfit, and he once again worked himself a yard on the edge of the area, this time getting a better shot away that rippled the side netting.
Fenerbahce had offered precious little throughout the first half, but they manufactured a huge lifeline on the stroke of half-time.
Filip Kostic marauded down the left wing, and his deflected cross found the unmarked Sebastian Szymanski, who sensationally swept a volley over a hapless Jack Butland, halving Rangers’ advantage and setting up an intriguing second half.
The pattern of play suggested it would be a long second half for Rangers, who were camped on the edge of their own box, although admittedly a wayward Talisca strike was Fenerbahce’s only true sighting of goal before the hour mark.
Once the Scottish side had weathered the storm, they started to reassert their authority on the game, coming close to re-establishing their two-goal cushion when a swift counter ended with Hamza Igamane forcing Irfan Can Egribayat into tipping his goal-bound effort around the post.
That save looked even more crucial just minutes later when the Turkish side drew level in the tie, with Szymanski this time turning home at the near post after Mert Muldur cut the ball back for him.
Both sides traded late chances to find a killer blow which would have won the tie, but neither could find it as extra-time beckoned.
Rangers' main joy came when they got the ball to the feet of Cerny, and he forced a stunning one-handed save out of Egribayat in the 100th minute when his curling left-footed effort needed tipping over the bar.
Rangers did most of the legwork in extra time, but James Tavernier’s free-kick was about as close as they came to finding a winning goal, with a stunning Egribayat save ensuring the game went to penalties.
A two-legged tie with Athletic Club awaited the winner of the penalty shootout, and when Dusan Tadic missed the very first penalty, Ibrox erupted.
That set the tone for the shootout, as Jack Butland saved another penalty before Hakan Yandas missed what proved to be the crucial spot-kick, booking Rangers’ ticket to Bilbao for the quarter-finals.
Flashscore Man of the Match: Vaclav Cerny (Rangers)