JOIN USTihinen strike nails AC Milan
There were no such problems for the other big guns as Real Madrid, helped by two more goals from Cristiano Ronaldo, Manchester United and Chelsea secured victories while Bayern Munich drew 0-0 at home with Juventus.
Milan won at Olympique Marseille in their group opener but have had a tough time domestically under new manager Leonardo with goals very hard to come by.
It was the same story on Wednesday with a sparse San Siro crowd whistling derision at their side's blunt efforts.
Their big names were shown up by the clever mid-air backheel of unmarked Finnish centre back Hannu Tihinen which put Swiss side Zurich on the way to a famous victory after 10 minutes.
Substitute Gianluca Zambrotta hit a post for Milan in stoppage time but an equaliser would have merely papered over the cracks from another poor display by the 2007 champions.
Both Milan and Zurich have three points and Real Madrid top Group C on six after two more goals from red-hot Ronaldo helped them to a 3-0 home victory over Marseille. It took Real almost an hour to break through but they did so emphatically with three goals in six minutes. Ronaldo opened the scoring and was awarded a fortunate penalty converted by Kaka before the Portuguese winger got the third to make it nine for the season since his move from Manchester United.
His former club are managing alright without him, although the Premier League leaders had to come from behind to beat VfL Wolfsburg 2-1 at Old Trafford. Bosnian striker Edin Dzeko headed the lively German champions into the lead 10 minutes into the second half but 35-year-old Ryan Giggs levelled with a deflected free kick.
United, looking inventive around the box after a sluggish start, clinched victory 12 minutes from time with a crisp shot by midfielder Michael Carrick.
“All the praise he's had over the years... there's nothing to add,,” United manager Alex Ferguson said of evergreen Giggs.
United top Group B with six points. Wolfsburg have three, as do CSKA Moscow after their 2-1 home win over Besiktas.
Chelsea produced a repeat of their first group game as a solitary goal by Nicolas Anelka was enough to win 1-0 at APOEL Nicosia.
The French striker, who got the only goal against Porto at Stamford Bridge, was on target after 18 minutes but Chelsea did little else against the Group D outsiders.
Porto bounced back well with a 2-0 home win over Atletico Madrid to leave the fancied Spaniards up against it with just a point after two games. Bayern Munich missed an opportunity to take early command of Group A when they wasted a stack of chances in their goalless home draw with Juventus.
Results: Group A: FC Bayern München: 0 drew Juventus: 0; FC Girondins de Bordeaux: 1 (Michael Ciani 83rd) bt Maccabi Haifa FC: 0
Group B: PFC CSKA Moskva: 2 (Alan Dzagoev 7th, Milos Krasic 61st) bt Besiktas JK: 1 (Ekrem Dag 90+); Manchester United FC: 2 (Ryan Giggs 59th, Michael Carrick 78th) bt VfL Wolfsburg: 1 (Edin Dzeko 56th).
Group C: AC Milan: 0 lt to FC Zurich: 1 (Hannu Tihinen 10th); Real Madrid CF: 3 (Cristiano Ronaldo 58th, 64th, Kaka 61 PEN) bt Olympique de Marseille: 0.
Group D: APOEL FC: 0 bt Chelsea FC: 1 (Nicolas Anelka 18th); FC Porto: 2 (Falcao 75th, Rolando 82nd) bt Club Atlético de Madrid: 0.