Levski, who have won the competition 25 times, booked their place in the quarter-finals by winning 7-6 on penalties after both games had ended goalless.
It was also the last major football match in Bulgaria this year.
A heavy police presence surrounded the game between the most popular clubs in the Balkan country. Emotions ran even higher than normal and the penalties were followed by a mass brawl on the pitch.
The fighting started seconds after Dutch defender Dustley Mulder scored Levski's decisive spot kick. CSKA's French-born Senegalese centre back Jackson Mendy was one of the most active players in the melee.
CSKA reacted with fury earlier when referee Tsvetan Krastev failed to award a penalty in the second half for what looked an obvious handball by Levski striker Dimitar Makriev.
"It was another outrage against a great club like CSKA," club president Alexander Tomov told reporters. "There was a clear penalty as the ball hit the hand of their player and it was going to be a shot on target.
"Our team completely outplayed Levski, we had at least six or seven scoring chances."