The home side claimed the initiative from the start in a fast and furious beginning but against the run of play suffered a serious set-back after 18 minutes after a monumental error from Thomas Delaney.
During a completely harmless situation in midfield, Delaney chose to kick the ball back to his keeper, Diant Ramaj, as he hadn't spotted Mathias Kvistgaarden in his own half.
The Brøndby attacking midfielder managed to get hold of the loose ball, rounded the keeper and cooly made it 1-0 to silence the crowd in the Parken stadium.
Things got even worse for the home side when Kevin Diks, who will leave FC Copenhagen for Borussia Monchengladbach in the summer, got injured after 21 minutes.
FC Copenhagen began the second half as they started the first one and were rewarded after 57 minutes when Elias Achouri stole the ball from Yuito Suzuki and launched a terrific stinging drive into the top left hand corner to restore parity.
This prompted FC Copenhagen to intensify the pressure but they couldn't create any clear-cut opportunities against a well-organized Brondby rearguard and instead the visitors won a penalty just before the end which Daniel Wass duly converted.
In injury-time the home side did get a chance to at least get a point for their efforts but Mohamed Elyounoussi wasted the opportunity, when Patrick Pentz pulled off a superb save to secure three points for the visitors.