The Finnish centre-back (pictured) expertly turned in a 10th minute corner with his heel while both feet were off the floor to hand the Swiss champions their first points in Group C.
Seven-times European champions Milan won at Olympique Marseille in their group opener but otherwise it has been another sorry start to the season under new boss Leonardo, with only one goal scored at home and just eight points amassed from six Serie A matches.
They again lacked penetration and were often forced to send hopeful balls into the box with even the introduction of Ronaldinho at halftime failing to have much effect.
Filippo Inzaghi had two golden chances but was consistently offside while strike partner Alexandre Pato continued to look off the pace at a half-empty San Siro, which still managed a loud chorus of whistles at halftime.
Substitute Gianluca Zambrotta rattled the post in injury time and the final whistle was met by stunned silence while the Zurich players danced on the pitch.
Clarence Seedorf also went close for the hosts with fierce drives but Zurich, who lost to Milan in the UEFA Cup last term, were equally dangerous on the break and could easily have doubled their advantage.
Home defender Kakha Kaladze was booked for pulling down Tihinen at another corner but because the ball was not yet in play, the referee did not award a penalty.
Brazilian Leonardo, previously technical director at Milan, replaced Carlo Ancelotti as coach at the end of last season when the Italian moved to Chelsea but he was immediately handicapped by the sale of Kaka to Real Madrid.
Milan, who have not won the Italian scudetto since 2004, had already stuttered under Ancelotti in the two years following their 2007 Champions League triumph.
Only a few new recruits arrived in a frugal close season but owner Silvio Berlusconi has still said he is dissatisfied with their start.
Leonardo said before the game that every coach was under discussion. Milan's next two Champions League games are against Real Madrid.
