Lewandowski's 10 goals since the start of the campaign equalled Gerd Mueller's tally from the 1968/69 and 1977/78 seasons with the Bavarians top on a maximum 21 points and Borussia Dortmund, in action against Darmstadt 98 on Sunday, on 16 in second place.
Bayern, who host Dinamo Zagreb in the Champions League on Tuesday, were struggling against their disciplined opponents until the Poland captain rose high to head in for the lead in the 51st minute, becoming the fastest foreign player to reach the 100 Bundesliga goal mark by achieving the feat in his 168th match.
Lewandowski, who found the net five times against VfL Wolfsburg in the midweek game, scored again in the 63rd minute. He rounded keeper Loris Karius for his 101st Bundesliga goal.
Winger Kingsley Coman added another five minutes later as Mainz buckled and Bayern stretched their stellar start to the season.
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"It is great to have kept another clean sheet to be top of the table and even have a lead of a few points," Bayern captain Philipp Lahm told reporters.
"It is difficult to keep winning in the Bundesliga, especially away and when your opponents play so well. But you could see that they ran out of steam in the second half and we got more space and with our quality we used it well."
Wolfsburg, who travel to Manchester United on Wednesday, failed to rebound from their heavy loss to Bayern, drawing 1-1 in the Lower Saxony derby against struggling Hanover 96 to remain in fourth place on 12 points.
Fellow Champions League club Borussia Moenchengladbach made it two wins in two matches under interim coach Andre Schubert by edging past VfB Stuttgart 3-1, completing the victory with a stoppage-time goal from Raffael, as they prepare to host Manchester City in the Champions League.
Bayer Leverkusen completed a second straight victory when they eased past Werder Bremen 3-0, inflicting a third consecutive loss on the northerners. Leverkusen, who travel to Barcelona next week, joined Wolfsburg on 12 points.
Hoffenheim chalked up their first victory of the season by beating Augsburg 3-1 with two goals from Germany international Kevin Volland to move up to 15th with five points.
(Reporting by Karolos Grohmann; editing by Toby Davis)
