After a lacklustre opening to the match, Brondby took the lead after 17 minutes when Benjamin Tahirovic controlled a pass from Noah Nartey inside the box and slotted the ball past a helpless Odense keeper Viljar Myhra into the net.
16 minutes later, the visitors doubled the lead when they capitalized on a huge defensive blunder from Odense defender Yaya Bojang, who delivered the ball straight across the goal into the feet of Nicolai Vallys, who had no trouble putting Brondby in solid control.
Two minutes from the interval, Brondby pounced on another dreadful error from Bojang, who was dispossessed, allowing Brondby to feed the onrushing Marko Divkovic, who curled the ball superbly into the left-hand corner.
From the start of the second half, play was halted when Brondby fans threw tennis balls and coins onto the pitch and revealed a banner saying "without us no TV-gold".
After 76 minutes, the home side were handed a minor lifeline when Wass saw red after a collision with Jann-Fiete Arp. However, despite their numerical disadvantage, Brondby managed to make it 4-0 when Filip Bundgaard lobbed the ball over Myhra following a mistake from James Gomez.
Shortly before the end, Gomez atoned for his error by reducing the deficit to 1-4, but OB couldn't prevent Brondby from taking a much-deserved win.