Despite the defeat, Brondby is still ahead of FC Copenhagen in the table with 31 points after 16 matches. AGF tops the table with 34 points.
The stadium was sold out, with 34,442 spectators in attendance at Parken, which was without away fans due to a ban.
The first half was dominated by two nervous teams who struggled to settle into their stylish stride, but the game was no short of intensity.
Mads Emil Madsen had the home team's best attempt with a long-range stinging drive, but Brondby goalkeeper Patrick Pentz made a classy save.
Brondby's Marko Divkovic tried a direct free kick just outside the box, but Dominik Kotarski was on hand to keep the game goalless.
Brondby's well-playing midfielder Noah Nartey came close to breaking the deadlock ten minutes after the break, but the ball went just wide of the post.
FCK full-back Junnosuke Suzuki continued the exchange of blows with a good attempt, but Pentz just got down to the attempt.
After 71 minutes, FC Copenhagen got the winner when Jordan Larsson converted a penalty after a VAR check confirmed that Frederik Alves had blocked an attempt from Elias Achouri with his hand.
The home side was content just to defend for the rest of the game as Brondby chased the equalizer, but despite several dangerous situations in front of Dominik Kotarski´s goal, FC Copenhagen held on for the win.