Nine-time European champion Real Madrid lost 2-1 at Borussia Dortmund; seven-time champion Milan's woeful season continued with a 1-0 loss at Malaga, while City blew a 1-0 lead on the way to a 3-1 defeat at Ajax, and Arsenal was humbled by a 2-0 home loss to German club Schalke.
"I prepared the players badly for this game," City manager Roberto Mancini said. "This defeat is my fault."
The day after Manchester United scraped a 3-2 win at home to Braga, the erratic form of Premier League teams was again thrust into the spotlight with City conceding sloppy goals and Arsenal's misfiring forwards being given a lesson in clinical finishing by Schalke.
Madrid defended in numbers but fell behind to Robert Lewandowski's goal late in the first half, but the lead lasted barely a minute with Cristiano Ronaldo equalizing from a deft lob.
Defender Marcel Schmelzer scored Dortmund's winner to extend Madrid's terrible record in Germany. The Spanish side has now lost 17 of 24 games in Germany against a German opponent— and the only win was a 3-2 victory at Bayer Leverkusen in 2000.
"It's a sensational evening, such as you can only imagine in your wildest dreams," Dortmund coach Juergen Klopp said.
Dortmund tops Group D with seven points, one more than Madrid. Ajax has three points, while City has one and is in real danger of a second consecutive group-stage exit.
"It was an incredibly difficult game. We also had chances to win," Madrid coach Jose Mourinho said.
Midfielder Samir Nasri gave City the lead after being set up by James Milner, but Ajax hit back with goals from striker Siem de Jong, defender Niklas Moisander and silky midfielder Christian Eriksen.
"We were able to play our own game," Ajax coach Frank de Boer said. "With our wingbacks we were dominant, and they couldn't find an answer for that."
Before the match, police riding horses dispersed numerous fans as they were about to fight and 25 people were detained.
Milan, which lost its past two Serie A matches to drop to 15th place in the standings, got one reprieve but not a second as Joaquin Sanchez made up for a penalty miss by scoring the second-half winner. The Spanish side is in control of Group C with nine points.
"Nobody imagined this. We didn't know what would happen each morning and look at what's happening now," Joaquin said. "I think all of Malaga made history today. Milan's not in its best moment but it's still a top club."
Milan is still in a decent position to qualify as it has four points, one more than Zenit St. Petersburg, which beat Anderlecht 1-0 at home thanks to Alexander Kerzhakov's second-half penalty — his 200th career goal. Anderlecht is last with one point.
Arsenal, meanwhile, did little to suggest it can challenge for an elusive trophy this season — at least not in the Champions League.
Arsene Wenger's team, without a trophy since 2005, meekly lost 1-0 away to Norwich last weekend, and Netherlands internationals Klaas-Jan Huntelaar and Ibrahim Afellay scored late goals as Schalke outclassed Arsenal to move top of Group B.
"We haven't played anything like we can ... we lack confidence on the ball for some reason," said Arsenal assistant coach Steve Bould, who took charge while manager Arsene Wenger completed his three-match touchline ban.
Arsenal's last home loss in the group stage of the competition came against Inter Milan in September 2003.
"If we'd escaped with a 0-0 draw, we would have been delighted," Bould said.
Schalke is on seven points — one ahead of Arsenal. Olympiakos on three points and Montpellier has one.
Greece striker Kostas Mitroglou scored the winner as Olympiakos came from behind to beat the struggling French champions.
Gaetan Charbonnier's first Champions League goal was not enough as Greece defender Vassilis Torosidis equalized in the 73rd and Mitroglou struck in stoppage time.
"For us, these three points are like gold," Olympiakos midfielder Giannis Maniatis said. "They will revive our European campaign."
In Group A, Porto beat Dynamo Kyiv 3-2.
Porto led 2-1 at halftime thanks to goals from Silvestre Varela and striker Jackson Martínez, either side of an equalizer from Oleg Gusev.
Nigeria striker Ideye Brown made it 2-2, but a late winner from Martinez kept Porto top of Group A with a maximum nine points — three ahead of PSG, which lost 1-0 away to Porto three weeks ago for its only defeat so far this season.
In Zagreb, France winger Jeremy Menez pulled the ball back for Zlatan Ibrahimovic to score his 11th goal of the season. Menez doubled the lead just before the break.
"We made some stupid mistakes and conceded two goals," Dinamo defender Domagoj Vida said. "PSG showed its class and used its opportunities."
Dynamo has three points, while Dinamo — which conceded a tournament record amount of goals last season — has none after losing its ninth straight Champions League match.
French reports before the match said about 70 PSG fans had been intercepted on the border between Croatia and Slovenia in hire cars they had rented from Italy.
French police had provided Slovenian border officials with files on several hundred known hooligans from PSG, with about 150 expected to be travelling to Zagreb without tickets.