The successful Norwegian club entered the second leg with a 3–0 lead after the first match at home.
The Portuguese won the second leg 5–0 after extra time - and advanced 5–3 on aggregate.
"An epic comeback. Now the quarter-finals await. Bodø/Glimt can't breathe. It was crazy," writes Portuguese Record, according to Danish Ekstra Bladet.
One of the headlines in the Norwegian Dagbladet read "slaughtered" - while VG called the result a "brutal exodus".
Sporting will face Arsenal in the quarter-finals.
