AGF as well FCM showed a lot of will throughout the match in their quest to position themselves favorably in the top fight.
AGF dominated most of the possession in the first half, however, without being able to create any clear-cut opportunities.
Tobias Bech had a header which went just wide, but the visitors had by far the biggest opportunity of the half when Mikel Gogorza was put clean through but Jesper Hansen reacted quickly to keep the match goalless.
While AGF enjoyed most possession, FC Midtjylland were overall most dangerous, but failed to turn any of their total of nine corners into goals before the interval.
AGF only won one corner in the first half, but they didn't waste any time making the most of the next one four minutes after the break, when Patrick Mortensen again was at the right place at the right time to steer a deflected ball into the roof of the net.
However, AGF only had 16 seconds to enjoy their lead, as FC Midtjylland immediately almost restored parity, when Mikel Gogorza broke into the box and lifted the ball into the roof of the net past the reach of Jesper Hansen.
FCM pushed for a win in the final phase, and Oliver Sorensen and Adam Buksa in particular had huge chances to turn the tide in their favor but on both occasions Jesper Hansen kept the home side in the game with superb reflex saves.
FC Copenhagen maintains top spot in the league despite the defeat against Brondby earlier on Sunday. FCK has 47 points, FCM Midtjylland one less, while Brondby and AGF are on 42 and 40 respectively and can't be dismissed in the race for the title.