Home captain Stilian Petrov became the second player from his country to reach 100 caps, following Bulgarian Football Union president Borislav Mihaylov (102), but was unable to inspire his side to their first home victory over the Swiss.
"This is not a good result for either team," said visiting coach Ottmar Hitzfeld. "Bulgaria outplayed us in the first 30 minutes and I was impressed with the way their players controlled the game.
"But then we created some opportunities and unfortunately we couldn't score. Now we need a little miracle to reach the finals."
England, who won 2-0 in Wales on Saturday, and Montenegro are joint top of the group with 10 points from four games.
Switzerland are third and Bulgaria fourth, both with four points from as many matches.
Bulgaria, chasing their first home win in the qualifying campaign, began brightly with Ivelin Popov shooting just wide in the first minute and Dimitar Makriev going close with a header.
SOLO RUN
Aston Villa midfielder Petrov could have marked his century with a goal but blasted the ball over the bar after a fine solo run and cross from Popov.
Switzerland also had their chances, with skipper Alexander Frei's bullet header being parried by keeper Nikolay Mihaylov on the half-hour.
Bulgaria were again the livelier side after the break and Stanislav Manolev went narrowly wide with a header while Spas Delev tested keeper Marco Woelfli with a snap shot from the edge of the penalty area.
"We played well but couldn't achieve the right result," said Bulgaria coach Lothar Matthaus. "I always remain optimistic until the very end but we have to accept we no longer hold our fate in our hands.
"It was a game between Bulgaria and Switzerland and not between me and Ottmar Hitzfeld," added Matthaus referring to his fellow German. "But it was a pleasure for me to face him."
