(CNN) -- Jose Mourinho's quest to become the first coach to win Europe's Champions League with three different clubs got off to a winning start as Real Madrid beat Ajax 2-0 in their opening group game on Wednesday, while Arsenal thrashed Braga 6-0.
Charismatic Portuguese coach Mourinho inspired Porto to Champions League glory in 2004 and repeated the feat with Inter Milan last season, delivering the Italian club's first triumph in the competition since 1965.
He was hired by Real in June with the brief of breaking Barcelona's grip on the Spanish league title and landing the club's first Champions League trophy since 2002, and 10th in total.
Opening their campaign at home in the Santiago Bernabeu stadium, Real took the lead against four-time winners Ajax when Vurnon Anita bundled a corner into his own net under pressure from Gonzalo Higuain.
The Spaniards struggled to make their dominance tell until the 73rd minute when Higuain followed up Mesut Ozil's shot and turned the ball into an empty net.
Real, who have not got beyond the last 16 for six seasons, racked up a total of 35 shots in the match.
"We should have scored many more goals but the team was compact and well organized," Mourinho told Sky Sports. "The team is improving step by step and the goals will come."
In the other game in group G, Swedish striker Zlatan Ibrahimovic scored his first two goals for AC Milan in the space of three minutes as the seven-time winners defeated Auxerre 2-0.
Swedish striker Ibrahimovic, who signed from Barcelona in the close-season, has now equaled Hernan Crespo's record of scoring for five different clubs in the competition.
In Group H, a Cesc Fabregas-inspired Arsenal destroyed a Portuguese side making their Champions League debut.
Arsenal went ahead with a Fabregas penalty after eight minutes and Andriy Arshavin doubled the lead with a low drive on the half hour.
Moroccan striker Marouane Chamakh latched on to a flick from Jack Wilshere to make it 3-0 before half-time, Fabregas added a fourth with a header, and substitute Carlos Vela added two more goals.
"I'm a bit disappointed because I wanted a hat-trick," Fabregas told ITV1. "It's something I still haven't done as a professional. But it was a good performance, really good."
Ukrainian club Shakhtar Donetsk are second in the group after beating Partizan Belgrade 1-0.
English champions Chelsea went 3-0 up inside half an hour against Slovakian outfit Zilina. Michael Essien scored the first after 12 minutes and Nicolas Anelka added two more goals before Daniel Sturridge notched a fourth after the break. Tomas Oravec netted a consolation goal for the hosts after a mistake from Petr Cech.
"The first half was fantastic. We played very well on the counter-attack," Chelsea manager Carlo Ancelotti told Sky Sports. "The second half was different but we had control of the match."
Marseille, the French champions and 1993 winners, suffered a surprise 1-0 loss at home to Spartak Moscow.
In Group E, 2009 finalists Bayern Munich left it late to make the breakthrough in a 2-0 victory over Roma. Thomas Mueller broke the deadlock after 79 minutes and striker Miroslav Klose added a second goal four minutes later.
Romanian side CFR Cluj scored twice in the first 12 minutes in their 2-1 victory over Basel.