Madrid forward Cristiano Ronaldo beat goalkeeper Joe Hart in the 90th minute to cap a dramatic comeback as the Spanish champions twice came from behind for a morale-boosting victory over the English champions following a week of domestic disarray.
While Madrid showed its pedigree as nine-time champion against its rich and ambitious opponent, AC Milan's comparable history in European competition couldn't help it shake off its early season troubles as it was held to a 0-0 draw at home by Anderlecht.
Also, Robert Lewandowski scored late as Borussia Dortmund kept pace with Madrid in the tough Group D with a 1-0 win over Ajax.
Arsenal shook off its poor away form in the competition to win 2-1 at French champion Montpellier, while Schalke also opened Group A with a 2-1 road win at Olympiakos.
FC Porto won 2-0 at Dinamo Zagreb while Malaga thrashed Zenit St. Petersburg 3-0 in its competition debut.
City hoped to get off on the right foot after missing out on the knockout stages last season. The big-spending Premier League club certainly had its chance only to come undone against a dogged opponent desperate for a victory to put its recent glum form behind it.
"The most important thing was to win and we did that. The team is good, the fans are good and I'm good," said Ronaldo, who returned to the Santiago Bernabeu for the first time since saying he felt "sad" at the club. "It was a crazy game."
City had done well to soak up Madrid's pressure in the first half before twice taking the lead in the second.
"It is difficult not because we lost — we can lose against a side like Real Madrid — but because with four minutes to go it was 2-1," City manager Roberto Mancini said.
Madrid's weakness on set pieces again proved costly as Aleksandar Kolarov curled home a free kick in the 85th minute to re-establish the visitors' advantage after Marcelo had cancelled out Edin Dzeko's 68th-minute opener.
Madrid came roaring back, however, as substitute Karim Benzema squeezed home an 87th-minute equalizer past Hart, before Ronaldo capped the comeback as the hosts responded to strong criticism from its coach and fans regarding its poor start to the domestic season.
Ronaldo, who refused to celebrate when scoring in his last home game, didn't hesitate to do so this time and neither did coach Jose Mourinho.
"I recovered my team, now I just hope I don't lose it," Mourinho said.
Dortmund's Lewandowski controlled the ball in the penalty area before hammering home a shot with three minutes remaining to reward the German club's late dominance and get its hopes of advancing rolling in the toughest group of the competition.
PSG's Zlatan Ibrahimovic became the first player to score for six different clubs in the competition as the French team attacked with gusto from the outset, eight years after its last appearance in the competition. The convincing win confirmed PSG's status as Group A favourite ahead of Porto.
"It's always important to win your first game in the Champions League," PSG coach Carlo Ancelotti said. "To play the way we did tonight can only be good for our confidence."
Ibrahimovic, who previously scored for Ajax, Juventus, Internazionale, Barcelona and Milan, netted from the penalty spot in the 19th for his sixth goal from six matches.
Brazil defenders Thiago Silva and Alex profited from terrible marking to put the home side 3-0 ahead after little more than 30 minutes, with Javier Pastore answering Miguel Veloso's 87th-minute consolation goal.
Seven-time champion Milan search for a positive result after its dismal start since Ibrahimovic's exit continued, as the Serie A club failed to rebound from losing its first two home games for the first time in 82 years. An error-strewn performance saw the Italian club's players jeered off the pitch by the more than half-empty San Siro.
"(The players) have to find a bit more confidence in themselves," Milan coach Massimiliano Allegri said.
Twenty-year-old Francisco "Isco" Alarcon scored twice and veteran striker Javier Saviola netted as Malaga went top of Group C with a rout in its Champions League debut.
Malaga, expected to struggle after heavy investment was cut off and players sold, instead dominated Zenit at its Rosaleda Stadium as the Russian club's big off-season signing Hulk failed to lift it to victory.
"The team has been through a rough time, but that is what I am most proud of, that the team has seen its way through it," Malaga coach Manuel Pellegrini said.
Elsewhere, Lucho Gonzales and Steven Defour scored late in each half as Porto secured its 150th European victory, beating Dinamo Zagreb, which has lost seven straight in the Champions League.
Lukas Podolski and Gervinho scored as Arsenal came back from Younes Belhanda's ninth-minute penalty within 11 minutes for a positive result for a club that had lost eight of its past 11 away games in the tournament. Arsenal coach Arsene Wenger watched from the stands as he served the first game of a touchline ban.
Benedikt Hoewedes and Klaas-Jan Huntelaar scored as Schalke ended Olympiakos' 10-year unbeaten run against German opponents on Greek soil in the Champions League. Djamel Abdoun levelled for Olympiakos in the 68th before Germany striker Huntelaar equalized one minute later.
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