Given the stadium’s infamous placement just north of the Arctic Circle, many teams have underestimated the Norwegians at this time of year.
And having succumbed to a 95th-minute penalty in the first leg, the home side almost drew level on aggregate within just three minutes, when a teasing Ole Didrik Blomberg cross was almost diverted into his own net by Bart van Rooij.
Goalkeeper Lars Unnerstall prevented it from looping in, and he also spared his side again merely five minutes later, clawing away Jostein Gundersen’s powerful header from a corner.
Twente thought they were to be rewarded for a rare venture into the Bodo/Glimt penalty area in the 25th minute, claiming that Ricky van Wolfswinkel’s shot struck Villads Nielsen on the arm, but referee Alejandro Hernandez Hernandez pointed for a corner.
Just when the visitors believed their luck was out, Michel Vlap swung in the corner, which was diverted into his own net by Fredrik Sjovold to extend the Tukkers’ aggregate lead to 3-1.
Before the break, Jens Petter Hauge came closest to an equaliser with a planted header, only to become the latest Glimt man to be denied by Unnerstall.
Ten minutes into the second half, Kjetil Knutsen’s side did manage to draw themselves level, thanks to an intervention from VAR, which spotted a clip inside the box from Gustaf Lagerbielke on Hakon Evjen.
Eying up his fourth goal of the competition, Kasper Hogh coolly converted the penalty down the middle to level the score on the night.
Lagerbielke almost made amends as the match entered the final 20 minutes, meeting a corner at the back post, but his header ricocheted off the post. In that moment, the home side’s efforts to find a late winner looked to be falling short against resolute defending from Joseph Oosting’s side.
That was until the second minute of added time. A cross from Brice Wembangomo took a deflection and was turned into his own net by Mees Hilgers.
The teams were set for extra-time, but no one told Wembangomo, who took aim from 25 yards just a minute later, to turn the tie around in the most dramatic fashion.
Twente threw bodies forward in a last-ditch attempt to save the tie, and amid bedlam in the Glimt penalty area, Sem Steijn forced the ball over the line to send the match to extra-time.
After the frantic finish to the 90 minutes, neither side was able to lay a glove on the other in the first period of extra-time.
But six minutes into the second period, a corner for the home side was knocked down by Odin Luras Bjortuft to Sondre Brunsted Fet, who swept the ball over the line before Steijn could clear it away.
The tie was finally wrapped up three minutes later when Fredrik Andre Bjorkan cut the ball across the six-yard box, and a touch from Arno Verschueren meant he scored the third own goal of the evening.
That sent the team from Enschede out with their first loss away from home in Europe this season. Bodo/Glimt, meanwhile, progressed from a European knockout tie having lost the first leg for the first time.
Flashscore Man of the Match: Brice Wembangomo (Bodo/Glimt)