Agger did not miss from 12 yards after Varazdat Haroyan brought down Viktor Fischer in the 73rd minute, placing the ball into the bottom left corner to beat Armenia goalkeeper Gevorg Kasparov. Haroyan was shown a red card for the challenge on Fischer after it earned him his second booking of the night - his first came in the second minute for a foul on Nicki Bille Nielsen.
Denmark dominated the game and had two early chances denied by Kasparov, who blocked a Bille Nielsen volley from the left of the area before saving Christian Eriksen's 20-yard effort.
Eriksen was again denied by the Armenia stopper just before the break, with Marcos Pizzelli wasting a rare chance for the home side when he sent a weak shot over the bar from distance just after the hour mark.
Denmark goalkeeper Stephan Andersen had little to do but he easily denied Aras Ozbiliz in the 72nd minute before a rash challenge by Haroyan changed the course of the game.
Andersen then produced a brilliant save in the dying moments to once again deny Ozbiliz from 30 yards, with Denmark claiming a crucial win.