The formidable attacking trio of Franck Ribery, Thomas Muller and Arjen Robben all struck as City was completely outplayed in UEFA Champions League Group D, although it also contributed to its own downfall.
Errors from goalkeeper Joe Hart and the defence proved costly but the host at least finished strongly as Alvaro Negredo replied and Bayern had former City defender Jerome Boateng sent off.
The result lifted Bayern clear at the top of the group and, even after just two games, probably left City in a battle for second place with its next opponent CSKA Moscow.
The overwhelming feeling was that a City side which thrashed Manchester United just 10 days previously was taught a footballing lesson.
Manuel Pellegrini was appointed by City in the northern summer in expectation he could improve the club's standing in Europe but this was clear indication of the scale of the task ahead.
Yet as brilliant as the German side was, the defence and Hart had a harrowing time.
Hart was at fault for Bayern's opener and was beaten too easily for the third goal, while Gael Clichy was the chief culprit for the second.
City seemed intent on making a lively start but it soon became apparent that Bayern had the class to boss the game.
It carved out an early opening as David Alaba was given room to cross but Robben was unable to direct a header on target.
City showed some promise as Jesus Navas crossed for Micah Richards but the defender, surprisingly recalled in place of Pablo Zabaleta for the fixture, headed at Manuel Neuer.
Bayern firmly took control of the match in the seventh minute as Ribery cut in from the left and unleashed a low swerving shot from the edge of the area which Hart failed to deal with.
It was powerful strike but after a relatively serene spell for club and country for Hart - keeping five successive clean sheets in August and September - it was a mistake that will provide untimely ammunition to critics ahead of England's climactic 2014 FIFA World Cup qualifiers.
Bayern oozed class thereafter, barely giving City a kick as it dominated possession and cut its way through the host with quick and incisive passes.
Remarkably, it yielded few clear-cut chances in the first half but Hart punched unconvincingly from an Alaba cross and Toni Kroos had a long-range shot deflected narrowly wide.
Robben picked up possession on the edge of the area and drove across goal but Muller was unable to turn in.
Alaba then shot at Hart and the rebound off Matija Nastasic also needed to be dealt with by the keeper but City could consider itself fortunate to reach the interval 1-0 down.
Bayern stepped up the pace after the break and Robben had a shot deflected wide from the edge of the area after more neat interplay.
City had also looked more determined after the resumption but its renewed spirit was killed off as Dante picked out Muller with a crossfield pass.
The City defence was simply caught flat-footed and Clichy stopped in expectation of an offside flag that never came, exposing Hart.
Muller seized the opportunity and rounded Hart to double the lead.
Just three minutes later the task was put completely beyond City.
Fernandinho lost the ball in midfield and Robben charged down the right, bypassing Clichy and wrong-footing Nastasic before beating Hart at his near post.
Muller hit the post as Bayern threatened more but City finally found some bite late on.
James Milner had a shot tipped over and fellow substitute Negredo pulled one back with a powerful shot off the post 11 minutes from time.
Boateng was shown a straight red card after halting a Yaya Toure burst on the edge of the area and David Silva curled the resulting free-kick against the bar.
Negredo also headed wide as City gave itself some encouragement for the remainder of the campaign.
Group D rival CSKA Moscow drew level on points with Manuel Pellegrini's men after beating Viktoria Plzen 3-2 in St Petersburg.
Plzen goalkeeper Matus Kozacik's error allowed Radim Reznik's 78th-minute backpass to slip under his foot, and it proved to be decisive.
Cristiano Ronaldo helped Real Madrid establish a stranglehold on Group B with a double in a 4-0 demolition of FC Copenhagen.
Ronaldo, who scored a hat-trick in Real's 6-1 opening day victory over Galatasaray, and Angel di Maria both struck twice as the Spanish side swept the visitor aside at the Santiago Bernabeu.
The Portugal international marked his 100th appearance in European club football with a 21st-minute header, and then doubled his tally 20 minutes into the second half before Di Maria sealed the win with two goals inside the final 19 minutes.
Real stands four points clear of second-placed Juventus, which was denied victory in a dramatic conclusion to its 2-2 home draw with Galatasaray.
Didier Drogba's first-half strike had given the Turkish outfit the lead, but Arturo Vidal levelled with a 76th-minute penalty and substitute Fabio Quagliarella thought he had secured the points with a late header, only for Umut Bulut to equalise within seconds.
There was similar frustration for Manchester United, which looked to have put its domestic troubles to one side when Danny Welbeck headed it into an 18th-minute lead over Shakhtar Donetsk.
However, Taison's 76th-minute equaliser denied David Moyes a precious win, although he did become the first manager of an English club to leave the Donbass Arena in Europe's premier club competition with something to show for his efforts at the end of a 1-1 draw.
The two sides remain locked together on four points at the top of Group A with Bayer Leverkusen having closed the gap with a last-ditch 2-1 victory over pointless Real Sociedad.
Simon Rolfes put the German side ahead on the stroke of half-time and although Carlos Vela cancelled out his effort six minutes after the break, substitute Jens Hegeler curled home a brilliant stoppage-time free-kick to win it.
With the scores locked at 1-1, Leverkusen substitute Robbie Kruse was guilty of failing to make the most of a gilt-edged chance as time ran down, but Hegeler spared his blushes when he despatched his last-gasp effort into the top corner.
There were no such difficulties for Group C leader Paris Saint-Germain or Olympiacos as both clubs eased to 3-0 victories.
Star striker Zlatan Ibrahimovic claimed a double either side of defender Marquinhos's effort as PSG wrapped up the points against Benfica inside the opening 30 minutes.
But Olympiacos frontman Kostas Mitroglou went one better as he plundered a hat-trick to see the Greek side past Anderlecht in Belgium.
Mitroglu opened the scoring after 17 minutes, and then found the back of the net again 11 minutes after the restart before completing his treble with 18 minutes remaining.
UEFA Champions League Matchday 2 results:
Bayer Leverkusen 2-1 Real Sociedad
Shakhtar Donetsk 1-1 Manchester United
Juventus 2-2 Galatasaray
Real Madrid 4-0 FC Copenhagen
Anderlecht 0-3 Olympiacos
Paris Saint-Germain 3-0 Benfica
CSKA Moscow 3-2 Viktoria Plzen
Manchester City 1-3 Bayern Munich