The Danish favorites went into the return leg with a mountain to climb when they suffered a 3-0 defeat in the first leg in the Icelandic capital, in one of the most humiliating moments in Danish football club history.
But if things were already looking bleak for Frederik Birk's men heading into the return leg, bad turned to worse for the home side when Clement Bischoff was sent off after stamping on Tarik Ibrahimagic after 17 minutes.
Brondby subsequently struggled to create chances against a well-organized Icelandic rearguard until the 45th minute, when Nicolai Vallys, on the brink of half-time, handed the home side a lifeline with a strong header from a wonderful delivery from Mats Köhlert.
The goal visibly gave Brondby belief and they used their momentum to double their lead seven minutes after the restart when Vallys again was on target as he volleyed home Sean Klaiber's well-timed delivery.
Just five minutes later Brondby restored parity in the aggregate scoreline, when Mats Köhlert latched on to a superb inside pass from Vallys to set up the on-rushing Filip Bundgaard who slid the ball into the net from close range.
Most spectators could probably hardly believe what unfolded in front of their eyes and Bundgaard completed an all together dismal night for the visitors when he made it 4-0 after 71 minutes on a superb long-range stinging drive.
Brondby can now look forward to facing Strassbourg in the playff round for the league phase.