Schalke suffered a second-half meltdown against Wolfsburg while Borussia Monchengladbach and Bayer Leverkusen recorded wins
Mario Mandzukic's goal after 13 minutes was enough to ensure Pep Guardiola's men kept up their winning start to the season at the Commerzbank-Arena having beaten Borussia Monchengladbach in their first game.
However, the result leaves Frankfurt propping up the table on goal difference after their 6-1 thumping at the hands of Hertha Berlin in their opener.
Leverkusen also enjoyed a 1-0 win but needed a first-half own goal from Daniel Schwaab to secure all three points at Stuttgart and move them joint-top with Bayern.
Braces from Roberto Firmino and Anthony Modeste helped Hoffenheim to a 5-1 victory over Hamburg, and that emphatic scoreline was enough to push Markus Gisdol's fifth in the table - two points behind Werder Bremen, who also gained three points.
Mehmet Ekici's goal after 23 minutes was enough to give them the win against Augsburg, who remain in 17th place without a win or a goal so far in 2013-14.
Elsewhere, Schalke's disappointing start to the season continued, as they conceded four goals in 35 second-half minutes away at Wolfsburg.
Gladbach bounced back after their opening-day defeat at the Allianz Arena to hit three past Hannover without reply. Max Kruse, Christoph Kramer and Filip Daems were the men on the scoresheet for Lucien Favre's side.
Meanwhile, a late Sebastian Freis goal proved insufficient for Freiburg as they slipped to their second defeat of the season, losing 2-1 at home to Mainz.