Goals from Bastian Schweinsteiger and Thomas Muller put the Bavarians on the way to all three points and Mario Gomez allowed them to conserve their energy for the last 10 minutes with the third.
Sami Allagui then scored a consolation for Mainz, but Bayern held on without any problems for their second straight win.
Bayern started with wingers Arjen Robben and Franck Ribery in their side for the second week running.
And the outcome was the same as last weekend's emphatic 4-0 triumph over Hoffenheim.
The pair were both involved in setting up Schweinsteiger for the opening goal in the ninth minute.
Ribery's cross from the left was headed back across goal by Robben and Schweinsteiger nodded in from close range.
It was almost two within a minute as Robben raced down the wing and squared the ball to Muller, who lifted his shot high over the crossbar.
Mainz had the chance to level after 27 minutes when Andre Schurrle was sent through and he lobbed the ball over the onrushing Thomas Kraft, but it finished the wrong side of the post from the home side's point of view.
Robben and Ribery then combined again to create Bayern's next chance in the 38th minute, but the latter's shot was deflected behind.
Kraft ensured Bayern went in at the break ahead by denying Schurrle with an excellent save in the closing stages of the first half, but his exertions and an earlier knock to the head meant he did not reappear for the second half. Hans-Jorg Butt took his place in the Bayern goal.
Bayern doubled their lead five minutes into the second half with Robben lifting the ball up for Muller inside the area, and he provided a composed finish.
Gomez wrapped up the win for Bayern in the 77th minute, lunging in to provide the finishing touch to an excellent team move which also involved Muller and Ribery.
Allagui got on the scoresheet for Mainz in the 84th minute when he rose to head in Christian Fuchs' cross from six yards out, but it was scant consolation as Bayern responded to Borussia Dortmund's win earlier in the day by returning to 13 points adrift of the league leaders.