The Bulgarians came to pack men behind the ball and threaten on the counter-attack, a tactic they employed to good effect grabbing the crucial away goal in the 23rd minute.
Velizar Dimitrov ran onto Aleksandar Tomovski's pass to fire past Brad Friedel and send the travelling Bulgarians into raptures.
Graeme Souness professed before the match that "the UEFA Cup is a poor second in our priorities to the Premiership" and his team selection vindicated this, making six changes from Sunday's draw against Manchester City.
It seemed they had a mountain to climb but an equaliser just four minutes later arrived courtesy of Corrado Grabbi.
Nils-Eric Johansson raced down the left before pulling back a low cross for Grabbi to lash in off a post.
However, CSKA should have retaken the lead just two minutes later when Andy Todd's dreadful error allowed Macdonald Mukasi a great opportunity but Friedel made a fine block.
A poor game was enlivened in the second half by the dismissal of Tomavski for his second bookable offence and also a spate of cautions, seven overall.
Blackburn striker Dwight Yorke was forced to leave the action after only 12 minutes, giving Souness' side more injury problems ahead of a crucial Premiership game with Leeds on Saturday.
Souness said after this disappointing draw: "This tie is not over yet." However, a tough game in the Bulgarian capital is not what his injury-hit side need at this precise moment.