On Sunday, in-form OB looked far from the team that had come into the match unbeaten in six matches.
AGF heavily dominated the match before the break, and after 13 minutes, Patrick Mortensen easily put the hosts 1-0 up from close range after a falt cross from winger Rasmus Carstensen.
The same Carstensen then also set up Kristian Arnstad, but the Norwegian headed his great chance straight at OB goalkeeper Theo Sander.
However, the home side still managed to double the lead before the interval when Gift Links, after a smart run by Felix Beijmo, had space to curl the ball beautifully into the left hand top corner from the edge of the box.
AGF continued their dominance in the second half without being able to put the match beyond doubt.
Instead the visitors managed to reduce the deficit five minutes from the end when Noah Ganaus turned in a cross from Adam Sorensen.
The match looked to headed for extra-time with the two sides even on aggregate when Links and Arnstad then combined to set up Beijmo at the back post to sent the crowd into a frenzy.
In the other Cup return leg played on Sunday, FC Nordsjaelland won 2-1 against FC Midtjylland but it was far from enough to secure access to the semi-final as Mike Tullberg's had already one 5-1 in the first leg.