A classy goal by Finnish defender Hannu Tihinen piled on the misery for AC Milan as FC Zurich won for the first time in this season's Champions League.
Tihinen got behind Milan Gajic's cross from the right and back-heeled the ball into the back of the net after 10 minutes.
The Rossoneri enjoyed a hatful of chances to level the score but failed to finish them off.
The outcome saw Zurich bounce back from their 5-2 humiliation at the hands of Real Madrid in their Group D opener.
Milan coach Leonardo went into the game under pressure with growing discontent at the San Siro following the Rossoneri's lacklustre performances on the domestic front.
With just two wins in six Serie A encounters, the out-of-form Milan were aiming to chase their blues away with a second Champions League win.
Leonardo played with Clarence Seedorf in support of attacking duo Filippo Inzaghi and Pato.
Inzaghi, who stole the limelight with a brace in their 2-1 win over Marseille in their group opener, was unable to deliver this time.
The visitors could not have asked for a better start as they broke the deadlock early on.
Milan should have restored parity shortly after, but Inzaghi fired wide from Marek Jankulovski's fine cross.
Midway through the first half, Zurich almost extended their lead with Xavier Margairaz's right-footed effort from the edge of the area going just inches wide of the far post.
At the other end, Inzaghi latched onto Abate's cross from the right but his header went wide.
Shortly before half-time, Seedorf tried his luck from the distance and his effort almost surprised Zurich goalkeeper Johnny Leoni.
Leonardo made a double substitution after the re-start with Ronaldinho and Gianluca Zambrotta entering the pitch.
But Milan struggled in the early stages of the second half against Zurich's well-placed defence.
On the hour mark, Inzaghi should have equalised but his powerful header from Andrea Pirlo's assist was denied by a great save from Leoni.
Ronaldinho's through ball found Pato inside the area, but he failed to beat Leoni one-on-one with the Brazilian firing wide as another chance went by for the Rossoneri.
Milan continued to surge forward and Inzaghi came close with a left-footed strike from the heart of the area which was saved by the keeper.
Zurich reacted and Milan goalkeeper Marco Storari was forced to fully stretch to parry Margairaz's angled strike from the edge of the area.
Ronaldinho and Zambrotta tried their luck from the distance but both their efforts went high and wide as Milan fans grew impatient.
Inzaghi then got behind Pirlo's cross but his right-footed strike from the centre of the area went just high over the bar.
The Rossoneri did not give up hope and their efforts were almost rewarded with two minutes remaining.
Massimo Ambrosini's stinging drive from the distance beat Leoni but struck the far post as Zurich held on for the victory.
