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, although the home side were unfortunate to have a goal disallowed before half-time.
Bayern also had a goal disallowed in the second half and missed several chances to make it a more comfortable win as they were made to sweat until the final whistle.
Mario Gotze was left on the bench a week after appearing in Bayern shirt for the first time in a friendly win against Gyori, and he was ultimately not called upon by Guardiola as his side struggled slightly more than he probably expected.
His designated place was instead given to Xherdan Shaqiri, who proved to be Bayern's most dangerous outlet as they immediately showed who was boss.
Dominant in the possession stakes, Bayern also carved out some good early chances before Mandzukic put them in front in the 13th minute, turning Thomas Muller's cross in from six yards out.
Frankfurt tried to respond immediately with the Bayern defence looking stretched for a moment, but they soon regrouped to avert the danger.
One of those, defender Dante, had Bayern's next best chance to score in the 33rd minute, but his shot from six yards out was saved instinctively by Kevin Trapp.
Frankfurt ended the first half well and should have gone in at half-time level when Meier headed the ball in from a matter of inches, but the linesman's flag was controversially raised.
The home side looked more confident in the second half, having managed to keep Bayern down to just one goal in the first 45 minutes, and Guardiola's men were forced to do some defending of their own.
Manuel Neuer was nearly left with egg on his face when he raced off his line and was beaten to the ball by Srdjan Lakic, but he lost his balance and was unable to get enough power on his shot to send it into the open goal.
Bastian Schweinsteiger had the chance to ease Bayern's concerns, but his shot was blocked before Arjen Robben had a goal ruled out for offside.
There was late drama as Frankfurt pushed forwards, but Meier was unable to get the ball under control and ended up sending it weakly towards Neuer with his knee as Bayern held on.