(CNN) -- Cristiano Ronaldo scored two free-kicks on his European debut for Real Madrid, who opened their Champions League Group C campaign with a 5-2 victory away to FC Zurich on Tuesday night.
Cristiano Ronaldo has scored in every game he has played for Real Madrid so far this season.
Ronaldo, who became the world's most expensive player when he joined the Spanish club for $130 million from Manchester United in July, put the visitors ahead in the 27th minute and then sealed victory on 89 as the Swiss side sought to level at 3-3.
AC Milan also got off to a winning start in Wednesday's other Group C game, winning 2-1 away to Marseille thanks to goals in each half from veteran striker Filippo Inzaghi.
Real, unbeaten this season under new coach Manuel Pellegrini, romped to a 3-0 lead at halftime.
Winger Ronaldo settled any early nerves with his first set-piece -- a spectacular effort which goalkeeper Johnny Leoni got a hand to -- after being himself fouled, then the Portugal star was involved as Raul doubled the lead in the 34th minute.
Ronaldo deftly headed the ball through to Gonzalo Higuain, whose scuffed shot was diverted into the net by the veteran captain for his 65th goal in the competition.
Higuain made it 3-0 just before halftime as he was sent clear, and this time made no mistake as he fired the ball low past Leoni.
Real suffered a scare when Zurich scored twice in two minutes after the break, as the expensively-assembled team's fragile defending again became apparent.
Xavier Margaraiz pulled one back from the penalty spot on 64 after goalkeeper Ikar Casillas was ruled to have fouled Alexandre Alphone, despite minimal contact, then Silvan Aegerter darted in unmarked at the near post to glance a header in from a left-wing corner.
The home side poured forward in search of an equalizer, with Lassana Diarra becoming the sixth Real player to be booked as his team's frustration boiled over.
But Leoni let Madrid off the hook in the 89th minute when he fumbled Ronaldo's long-range free-kick into the net despite getting both hands on the ball.
Guti then added a delightful chip when he was set free on the counterattack in the third minute of time added on, resulting in a slightly flattering winning margin for Real, who next host Marseille on September 30.
Milan, at home to Zurich on that Wednesday, shook off their poor early domestic form to win the rematch of the first Champions League final in 1993.
The Serie A side, who lost that match 1-0, took the lead in the 28th minute when Clarence Seedorf -- who started ahead of Ronaldinho -- cut in from the left and delivered a right-foot cross to set up the unmarked Inzaghi from close range.
Marseille leveled five minutes after halftime when former Real defender Gabriel Heinze headed home Benoit Cheyrou's free-kick.
But Inzaghi, making his first start this season, netted the winner with 15 minutes to go as he got in front of his marker to volley in his 61st European goal from another cross by Seedorf.
In Group D, Chelsea beat Porto thanks to a 48th-minute winner from striker Nicolas Anelka, while Spanish side Atletico Madrid were surprisingly held 0-0 at home by Apoel Nicosia of Cyprus.
Anelka started up front in a lone role in the absence of the suspended Didier Drogba, who will miss Chelsea's first three games for abusing the referee during last season's semifinal defeat by Barcelona.
He broke the deadlock after Salomon Kalou poked the ball towards the penalty area after slipping on the wet surface, and the France forward found the net from an acute angle when goalkeeper Helton parried his initial shot.
Chelsea then needed goalkeeper Petr Cech to make several saves to deny Porto, who had Fernando sent off late in the match for a second yellow card.
Atletico continued their poor start to the season as Apoel came away from the Spanish capital with an unexpected point.
Goalkeeper Dionisis Chiotis produced several fine saves to keep out the home team, including a spectacular long-range shot from captain Diego Forlan, who also hit the crossbar with a fierce free-kick.