Cristiano Ronaldo struck the first for Real, who will host this season's final, and the 80 million pounds new boy helped them recover from a nasty bout of nerves by adding a second free kick late in the Group C opener on Tuesday.
The tussle at the Letzigrund provided the best entertainment on the return of European football's elite club competition.
Manchester United, who lost to Barcelona in last season's final, squeezed a 1-0 win at Besiktas in Group B with a Paul Scholes header and Juventus were held 1-1 at home by Girondins Bordeaux in Group A.
A goal from striker Nicolas Anelka, beautifully taken after his first effort was beaten away, gave Chelsea a 1-0 home win over Porto in Group D while two goals from Filippo Inzaghi kept AC Milan on Real's heels with a 2-1 win at Olympique Marseille.
Milan's game at Marseille was a repeat of the first final of the Champions League era in 1993 but this was not to be a night of classic drama - apart from in Zurich, that is.
CRISIS-BUSTING INVESTMENT
Real brought in Ronaldo from Manchester United as part of an eye-watering investment of a quarter of a billion euros designed to buy them a ticket for their own end-of-season party at the Bernabeu.
Qualifying for the knockout phase should be a formality after this victory but the way they let the Swiss team give them a scare will give coach Manuel Pellegrini a lot to think about.
"They say we're favourites to win the Champions League but we have to take it step by step," Ronaldo told reporters after his two-goal European debut for the Spanish club.
Real, who won the last of their nine European Cups in 2002, appeared to be cruising when Ronaldo, Raul and Gonzalo Higuain scored in a devastating 18-minute spell before halftime but from 3-0 up they suddenly found themselves wobbling at 3-2.
The game turned when Xavier Margairaz converted a 64th-minute penalty after Iker Casillas upended Alexandre Alphonse and almost immediately Silvan Aegerter headed in to bring the game back to life.
Ronaldo snuffed out Zurich's comeback hopes with a free kick from longer range with a minute of normal time left, as keeper Johnny Leoni contrived to punch the ball into the roof of his own net. Guti then completed the scoring.
Bayern Munich took control in Group A with a 3-0 win at Maccabi Haifa, with young midfielder Thomas Mueller scoring two goals for the second time in four days following his double against Borussia Dortmund.
VfL Wolfsburg, the team who pipped Bayern to the Bundesliga title last season, had a Grafite hat-trick to thank for a 3-1 home win over CSKA Moscow in Group B.
APOEL Nicosia, like Wolfsburg and Zurich playing their first match in the Champions League, had an encouraging goalless draw at Atletico Madrid in Group D.
As Champions League debuts go, it is hard to beat a hat-trick and the Brazilian Grafite was ecstatic and hoping to take
