Real Madrid and AC Milan began their Champions League campaigns with 2-0 victories Wednesday, while English rival Chelsea and Arsenal opened with big-scoring wins. Real Madrid coach Jose Mourinho presided over the nine-time champion's triumph against Ajax in the same Santiago Bernabeu stadium where he won last season's final with Inter Milan. Milan, Madrid's biggest rival in Group G, beat Auxerre after two goals from new signing Zlatan Ibrahimovic. Cesc Fabregas and Carlos Vela each scored twice in Arsenal's 6-0 rout of Portuguese side Braga, while Nicolas Anelka's double helped Chelsea surge to a 4-1 victory over newcomer Zilina. Bayern Munich, beaten by Inter in the final in May, defeated AS Roma 2-0 in Group E. In the Spanish capital, Madrid went ahead in the 31st minute when midfielder Xabi Alonso's corner was deflected in by Ajax defender Vurnon Anita. The second goal took until the 73rd to arrive, with striker Gonzalo Higuain well placed at the far post to score from Mesut Oezil's cross. Madrid's finishing was poor but luckily it didn't prove costly. In the other group match, Ibrahimovic broke the deadlock in the 66th after linking up with Kevin-Prince Boateng and Ronaldinho. The Sweden striker's second came three minutes later. Chelsea maintained its superb start to the season, having opened its Premier League title defense with four wins, with an emphatic win in Group F despite the absence of suspended striker Didier Drogba. The visitors raced into a 3-0 lead inside 30 minutes against tournament newcomer Zilina. Anelka's cross was turned in by Michael Essien before the French striker hit two goals himself. Daniel Sturridge hit Chelsea's fourth in the 48th minute. Zilina's consolation goal came in the 55th when an unmarked Tomas Oravec pounced on the loose ball from Branislav Ivanovic's deflection after Cech had failed to hold on to a cross. In the other Group F match, defender Cesar Azpilicueta scored a late own-goal to give Spartak Moscow a 1-0 win at Marseille, which wasted several scoring chances. At Emirates Stadium, Fabregas scored his first Arsenal goal since March, hitting the target from the penalty spot in the ninth minute after Marouane Chamakh was fouled by Luiz Felipe. Fabregas provided the second, turning two defenders before slipping the ball through for Andrei Arshavin to score inside the near post in the 30th. Intricate passing between Arhavin and Fabregas led to Arsenal's third, with Chamakh striking from close range after being fed by Wilshere's back heel. Fabregas buried a free header from Arshavin's cross at the start of the second half, while Vela chipped in another in the 69th and vollyed in Arsenal's sixth late on. It was a closer match in the other Group H encounter, with Shakhtar Donetsk captain Dario Srna's second-half free kick giving the Ukrainian champion a 1-0 victory over Partizan Belgrade. The goals came quicker in the group's other match. Ionut Rada and Lacina Traore scored inside 12 minutes for Cluj, clinching a 2-1 victory over FC Basel, which pulled one back in first-half injury time from Valentin Stoker's header.