Mario Mandzukic's 13th-minute strike was enough for Pep Guardiola to follow up his maiden home win as Bayern boss with his first away victory, but they rode their luck as the home side were unfortunate to have a goal disallowed before half-time.
Bayern also had a goal chalked off in the second half and missed several chances to make it a more comfortable win as they were made to battle until the final whistle.
Bayer Leverkusen, Werder Bremen and Mainz also picked up wins on Saturday to continue their 100 per cent starts to the Bundesliga season.
A first-half Daniel Schwaab own goal earned Leverkusen a 1-0 success at Stuttgart while Bremen claimed victory over Augsburg by the same scoreline.
Mehmet Ekici's fourth goal for the club was enough to continue their perfect start to life in the league under new coach Robin Dutt, while Augsburg are still searching for their first points and first goals.
Mainz also made it two wins from two with a 2-1 victory over Freiburg, Niki Zimling and Nicolai Muller netting in quick succession in the second half before Sebastian Freis netted a consolation for the hosts.
Wolfsburg scored four second-half goals to pick up their first points of the campaign and dampen Schalke's preparations ahead of their Champions League play-off with PAOK FC on Wednesday.
Robin Knoche, Vieirinha, Naldo and Stefan Kutschke scored the goals for Dieter Hecking's men as they dismantled the Royal Blues at the VW-Arena in a 4-0 triumph.
Elsewhere, Roberto Firmino scored twice and set up his side's other three goals as Hoffenheim inflicted a 5-1 home mauling on Hamburg.
Firmino put the visitors in front after just five minutes with Rafael van der Vaart levelling from the penalty spot just before half-time.
Kevin Volland gave Hoffenheim the lead again early in the second half before Anthony Modeste grabbed a brace and Firmino supplied the finishing touch to an emphatic win for Markus Gisdol's men.
Also, Borussia Monchengladbach bounced back from defeat on the opening day with a 3-0 home victory over Hannover, the goals coming from Max Kruse, Christoph Kramer and Filip Daems.