Bundesliga wrap: Bayern topple gritty Frankfurt, Dortmund cruise
The German giants opened the scoring through Frenchman Franck Ribery on the stroke of half-time and although Anderson Bamba headed against the bar for the visitors, Jupp Heynckes' men doubled their advantage when David Alaba converted a controversial penalty on 76 minutes.
Bayern had begun the game brightly, as if intent to put the upstarts from Frankfurt firmly in their place. Indeed, the hosts could have been ahead inside eight minutes, Toni Kroos breaking down the left-hand side before dragging a ball across the six-yard box which a stretching Arjen Robben managed to get on the end of but could only divert into the side netting.
Frankfurt slowly began to impose themselves and had chances to draw level but Bayern raised their game just before the break and after Daniel van Buyten had a goal ruled out for offside, Ribery finally broke the deadlock, side-footing home at the far post after Javi Martinez had sprung the offside trap.
The game remained delicately poised throughout the second half until Alaba converted from the spot with 14 minutes remaining after Vadim Demidov had been harshly penalised for fouling Bastian Schweinsteiger in the area.
Unsurprisingly, Frankfurt kept fighting but they were unable to find a route back into the game and Bayern saw the game out quite comfortably to make it 10 wins from 11 league games this season.
Meanwhile, defending champions Borussia Dortmund returned to winning ways with a routine 3-1 victory over cellar-dwellers Augsburg.
Juergen Klopp's side ended their last league outing in a disappointing 0-0 stalemate at home to Stuttgart, but there were no signs of such a result repeating itself as the visitors strolled to a comfortable victory to see their fleeting title defence endure for another week.
German international Marco Reus continued his superb form with a ninth-minute free kick before a second-half brace from Robert Lewandowski kept Dortmund within 11 points of rivals Bayern.
In other results on Saturday, Schalke consolidated second position with a come-from-behind 2-1 win at home to Werder Bremen, Australia international Robbie Kruse netted his first goal of the season as Fortuna Dusseldorf drew 1-1 with Hoffenheim, while Freiburg and Hamburg played out a goalless stalemate.