Bayern Munich dominated Manchester City to take all three points at the Etihad Stadium, while Manchester United claimed a draw from their trip to Shakhtar Donetsk. Elsewhere, Real Madrid recorded another big victory as they faced Copenhagen, while Juventus were held at home to Galatasaray and Paris Saint-Germain won big against Benfica.
• Brewin: Three things - City v Bayern
Manchester City slumped to a 3-1 home defeat as Bayern Munich put on a masterclass to maintain their perfect start to the defence of their European crown.
Franck Ribery gave Bayern the lead after six minutes when his powerful shot beat Joe Hart at his near post, with the City goalkeeper getting a strong hand onto the effort but being unable to prevent the ball from hitting the back of the net.
Thomas Muller then doubled the lead for Bayern ten minutes into the second half as Hart was exposed at the back, with Gael Clichy suffering a lapse in concentration to leave the Germany international unmarked.
Arjen Robben added a third four minutes later as Hart was once again beaten at his near post. Alvaro Negredo came off the bench to net a consolation for City, spinning his marker and curling his effort beyond Manuel Neuer in the 79th minute.
Jerome Boateng was given a straight red card for bringing down Yaya Toure after denying the City man a clear goal-scoring opportunity, but from the resulting free-kick David Silva struck the crossbar.
David Moyes came within 15 minutes of a morale-boosting victory, but Manchester United were pegged back for a 1-1 draw against Shakhtar Donetsk in their Champions League Group A encounter in Ukraine.
Danny Welbeck had struck in the first half to put United ahead, but Taison equalised in the 75th minute to ensure honours were even. There was even a late scare for United as Taison's cross deflected off Chris Smalling, forcing David de Gea into a fine stop.
The match also saw Ryan Giggs become the all-time record holder for appearances in the competition when he came on as a substitute midway through the second half.
Cristiano Ronaldo and Angel Di Maria each scored twice in an impressive 4-0 victory over FC Copenhagen that saw Real Madrid take control of Group B.
The Portugal forward grabbed a hat-trick in a 6-1 demolition of Galatasaray on the opening night and needed little persuading to add two more goals to his tally at the Santiago Bernabeu.
He gave the Primera Division club an early lead with a firm header but, after he doubled the advantage from a spellbinding Di Maria cross midway through the second half, his Argentinian team-mate arguably stole the show with a classy brace of his own to settle the tie.
Substitute Umut Bulut denied Juventus the chance to come from behind and snatch victory as Galatasaray forced a 2-2 draw away from home.
Roberto Mancini, who replaced Fatih Terim as Gala coach on Monday, was not on the touchline in Turin but enjoyed his return to Italy as his new charges dominated the Serie A champions, opening the scoring through Didier Drogba in the first half.
Juve did find a way back into the tie when Arturo Vidal levelled from the penalty spot 14 minutes from time and substitute Fabio Quagliarella thought he had grabbed all three points when making it 2-1 with time running out.
Bulut powered home a late leveller, though, guaranteeing Galatasaray their first point in the group while ambitious Juventus have only two after their 1-1 draw with Copenhagen.
Zlatan Ibrahimovic bagged a brace as Paris Saint-Germain made it two wins from as many Group C matches after easing to a 3-0 win against Benfica.
The French giants scored all three goals inside the opening half an hour with Ibrahimovic's double sandwiched in-between young defender Marquinhos' close-range strike.
From then on, the home side seemed to take their foot off the gas, but it hardly mattered as they followed up their opening 4-1 triumph at Olympiakos with another comprehensive win.
Substitute Jens Hegeler curled home a brilliant injury-time free-kick to snatch a 2-1 victory for Bayer Leverkusen against Real Sociedad.
Hegeler struck in the second minute of stoppage time to secure an eighth successive win for Sami Hyypia's men at the BayArena after the visitors had come within seconds of claiming a first point of the Champions League campaign.
Former Arsenal frontman Carlos Vela had earlier fired home from close range after keeper Bernd Leno had saved his 51st-minute penalty, in the process cancelling out Bayer skipper Simon Rolfes' opener in first-half injury time.
Japan international Keisuke Honda's classy finish helped CSKA Moscow to a first Group D victory as they came from behind to beat Viktoria Plzen 3-2.
The Russians, who lost 3-0 at Bayern Munich in their opening fixture, trailed to Frantisek Rajtoral's fourth-minute strike at the Stadion Petrovskiy in St Petersburg with torrential rain in Moscow having forced them to move the fixture.
But Zoran Tosic's deflected 19th-minute effort, which ended a 398-minute wait for a goal for Leonid Slutski's men in all competitions, paved the way for Honda to fire them ahead ten minutes later with an exquisitely-placed shot.
Radim Reznik's unfortunate late own goal, for which an horrendous error by keeper Matus Kozacik was to blame, sealed the win, although opposite number Igor Akinfeev had a moment to forget in injury-time when he made a mess of punching clear a cross and Marek Bakos reduced the deficit.
Kostas Mitroglou's hat-trick fired Olympiakos to a 3-0 win in Belgium and inflicted a second successive Champions League defeat on Anderlecht.
Mitroglou gave Olympiakos a first-half lead, which was preserved by Aleksandar Mitrovic's penalty miss, and the Greece striker scored twice more after half-time to complete a comfortable victory that leaves his side second in Group C.