Despite several spells of promising play, the reigning Danish champions have yet to secure a win this Superliga season.
On Sunday, the Aarhus team was clearly superior to OB for virtually the entire match, yet they had to settle for a 2-2 draw after trailing 1-2 at halftime, despite creating a wealth of chances.
Consequently, AGF remains winless after four rounds of play. Three draws have yielded three points, while the single point moves OB up to a total of four.
James Bogere, who has been a revelation in the Aarhus attack this season, gave the home side the lead in the first half before German midfielder Jann Fiete Arp turned the match on its head with two goals totally against the run of play before the interval.
Rasmus Carstensen then restored parity late in the match for AGF, who, despite launching a virtual siege on the visitors' gaol couldn't find a winner.
It was a poor preview for Aarhus, who will host Benfica on Thursday in the playoff qualification for the Europa League, trailing 1-3 from the first match in Lisbon.
Only one goal was scored, but it was a magnificent one, as FC Midtjylland secured a 1-0 home victory over Randers FC in the Superliga on Sunday afternoon.
Just under half an hour into the match, Dario Osorio picked up a poor clearance from Randers at the edge of the penalty area. Osorio controlled the ball with his thigh and, in the same motion, volleyed it into the net.
It was not a stellar performance from the home side, and Randers created several good chances on the counter-attack, particularly in the second half.
Nevertheless, the team from Central Jutland managed to scrape a win and remains unbeaten in the Superliga after four matches, with ten points to their name.
Sunday's match was sandwiched between two crucial European fixtures for FC Midtjylland, who are facing Croatian side Rijeka for a spot in the Conference League league phase.