Sporting knew they needed a fast start, and they almost had it inside three minutes. Maximiliano Araujo jinked and weaved his way down the left touchline before standing up a cross for Francisco Trincao, who could only guide his header over the bar.
The forward was in again mere moments later, but his attempted lob drifted harmlessly wide, with Nikita Haikin stranded off his goal line.
This concerted barrage on the Norwegians’ goal came at a price, with Sporting wide open on the rare occasions that Glimt managed to break out.
The visitors’ first chance was a golden one, and it seemed to have fallen to the right man, but first-leg scorer Kasper Hogh could not apply the finishing touch to a lightning-fast attack.
And he was made to rue that wastefulness just beyond the half-hour mark, when Goncalo Inacio headed home from a corner to put the Portuguese champions ahead on the night.
The hard-earned breakthrough was very nearly undone from a corner at the other end, yet Odin Bjortuft’s effort bounced twice off the crossbar in improbable fashion.
Sporting continued to push in the second half, although Sondre Brunstad Fet could have caused Rui Silva a real problem if he had generated some more power with his strike shortly after the break.
His regret was amplified in the 61st minute, when the hosts cut the aggregate deficit to just one, as Pedro Goncalves tapped in after a square pass from Luis Suarez.
That changed the contest again, and Glimt’s defending became increasingly desperate as they edged closer to the finish line.
They looked as though they might manage it, but a hugely unfortunate VAR intervention changed everything, with Fredrik Andre Bjorkan adjudged to have handled the ball in the box, allowing Suarez to convert the penalty kick and restore parity to the tie.
Sporting had the bit between their teeth, and substitute Nuno Santos almost clinched it without the need for extra time, clattering his effort against the post from the edge of the box.
And it took less than two minutes of the extra period for Araujo to effectively settle the issue, catching Haikin out at his near post to complete the remarkable turnaround.
Substitute Rafael Nel then dispelled any remaining nerves in time added on, adding a fifth goal to put the result beyond doubt.
With that, Bodo/Glimt miss the chance to be the first Norwegian side to reach the UCL quarter-finals in 29 years, while Rui Borges’ men become only the fifth side in competition history to overturn a three-goal deficit, and the first since Liverpool’s triumph over Barcelona in 2019.
Flashscore Man of the Match: Maximiliano Araujo (Sporting)