The visitors had the better of the opening stages, and they were duly rewarded after 25 minutes when they scored two goals in four minutes thanks to midfield orchestrator Tobias Bech.
Bech was on target the first time after 21 minutes when Erik Kahl managed to find him deep in the Odense box to open the score for AGF. And then four minutes later, Bech found the net again when Gift Links turned provider for Bech against a hesitant Odense rearguard.
Things could have been even worse for the home side before the break as the woodwork denied an otherwise great attempt for Felix Bejimo after 29 minutes.
But instead of a 3-0 lead for AGF, OB reduced the deficit on the brink of half time when Mads Emil Madsen was adjudged to havve handled the ball in the box and Jan Fiete Arp converted the penalty shortly after.
The home side began the second half in optimistic fashion but as they failed to take advantage of a couple of half chances, AGF restored their two-goal lead after 57 minutes.
Kristian Arnstad set off on an amazing run from inside his own half and finished off with a superb long range stinging drive into the low left corner to bring the visiting fans to their feet.
The visitors then put the game effectively out of reach after 66 minutes, when Theo Sander couldn't hold on to a close range header from Patrik Mortensen and Mortensen could easily poke the rebound into the net for a 4-1 lead.
Gift Links then finished off a truly dismal evening for the hosts when he got on the end of a terrific delivery from Arnstad to complete a superb performance from the visitors.