Bodo immediately showed they were not prepared to simply sit back and hold onto their two-goal advantage, with Jens Petter Hauge passing forward to Hakon Evjen, who forced a save from Christos Mandas inside the opening seconds - albeit a comfortable one for the goalkeeper.
Lazio’s class began to shine soon after, though, as Nikita Haikin saved Pedro’s shot from a tight angle before the hosts found the breakthrough.
Gustav Isaksen did some nice work down the line before cutting back for Taty Castellanos, who delightfully flicked into the net as the Italians halved their aggregate deficit.
Lazio threatened to get on level terms in the tie before half-time as they gained momentum, with Mattia Zaccagni heading Mario Gila’s delicate cross off the top of the bar.
Bodo did have a chance to score themselves in added time, though, as Patrick Berg’s free-kick almost found the far top corner, only to be tipped over by Mandas.
However, the start of the second half reverted back to the norm, as Lazio continued to dominate, with Zaccagni going close again as his snapshot was saved well by Haikin.
However, Bodo knew that just one goal could put the tie to bed, and they almost got it just after the hour mark. Hauge found himself in space in front of the goal, but his effort was brilliantly tipped over the bar by Mandas.
Haikin then made a trio of saves to keep the deficit at just one, denying Pedro, Castellanos and Zaccagni in quick succession.
The latter also saw his free-kick well-stopped by Haikin in the dying minutes, but was helpless to stop substitute Tijjani Noslin from tapping home a dramatic goal in stoppage time after some head tennis in the box, as Lazio forced extra time.
It took 100 minutes for the Eagles to turn the tie around, as Matteo Guendouzi chipped for Boulaye Dia to head home from close range and put them in front on aggregate.
The drama did not end there, though, as Bodo remarkably pulled a goal back in the second half of extra time, with Andreas Helmersen heading down and out of Mandras’ reach.
Amazingly, the goalscorer was then sent off for a second bookable offence minutes later, and would not take a penalty in the resulting shootout.
Bodo went first but Hauge’s tame effort was easily saved by Mandas, while Dia sent Haikin the wrong way to give Lazio an immediate head start. Substitute Sondre Brunstad Fet did the same, before Loum Tchaouna saw his saved.
The visitors scored their next two penalties as Noslin missed in between, with Berg having the chance to send them through. Astonishingly, he blazed over, but Castellanos also missed as the Norwegians won the shootout 3-2 to cement their place in history.
Flashscore Man of the Match: Nikita Haikin (Bodo/Glimt)