The aggregate win seemed a logical outcome after a game that the home side controlled for the greater periods of the game against the Superliga's current league leaders.
After a shot on the post in the early parts of the game from Rasmus Carstensen, AGF struggled to handle the home team's energetic pressure.
The visitors made a series of errors in their build-up that could have proved costly, and FC Midtjylland wasted several opportunities to put themselves in front.
Turkish international playmaker Aral Simsir came close when he hit the woodwork after AGF goalkeeper Jesper Hansen had kicked the ball straight into the feet of an opponent.
The Midtjylland pressure on the ball continued after the break, but AGF still managed to take the lead after a little more than an hour.
The recipe was simple. A long pass from goalkeeper Jesper Hansen was flicked on by Janni Serra for the onrushing Kristian Arnstad, who delivered an accurate ball for Tobias Bech, who gave the visitors the lead with a low stinging drive, leaving Elias Olafsson no chance in the Midtjylland goal.
AGF managed to preserve the lead for about ten minutes until Han-Beom Lee flicked on a long throw for Brumado, who equalized with a finely struck volley into the far corner.
A slightly injured Patrick Mortensen then replaced Serra up front, and the experienced forward got a huge chance eight minutes before time to keep his team alive.
Kevin Yakob delivered a superb ball across the face of the goal, where Mortensen arrived at the back post, but when it seemed easier to score, Mortensen had a poor touch and missed the open net to the astonishment of the travelling away supporters.
The missed chance took the final sting out of AGF's pressure for an equalizer, and time ran out without the home team's goal being seriously threatened.
