The reigning cup winners had an excellent chance of reaching another final, but blew a 3-0 lead in the first of two semi-finals on Wednesday.
The visitors were already ahead after eight minutes, when Anders Klynge provided a terrific through-ball for Andreas Poulsen to give Silkeborg a shock lead to silence the partisan Brondby crowd.
After 15 minutes the home side were hit by a further blow, when Brondby playmaker Nicolai Vallys was forced to leave the field with an injury.
Bad then turned to worse for the home side after 34 minutes, when Brondby-keeper Patrick Pentz poked a cross from Jens Martin Gammelby on to the legs of Jordi Vanlerberghe who couldn't prevent the ball from rolling into the net.
Seconds before the interval Silkeborg's leading goalscorer Tonni Adamsen then made it 3-0, when he finished off a creative attacking move.
From the start of the second half, coach Frederik Birk put Clement Bischoff, Sean Klaiber and Frederik Alves on the pitch to boost the home side's attacking strategy and it helped.
After 57 minutes Marko Divkovic threw the visitors a lifeline, when he broke into the left side of the Silkeborg box to fire the ball past Nicolai Larsen and into the net.
Brondby launched a virtual siege on the Silkeborg goal and were rewarded after 81 minutes, when Mathias Kvistgaarden headed home a pin-point cross from Clement Bischoff.
And only three minutes later Kvistgaarden was again on target, when another cross from Bischoff was deflected by Robin Ostroem into the path of Kvistgaarden, who completed an unlikely comeback.