Robert Lewandowski continued their perfect start to the Bundesliga season with a 2-0 triumph at Werder Bremen.
Poland captain Lewandowski netted two goals in four minutes in the final quarter against the spirited hosts to make it two wins from two for Carlo Ancelotti's side, who opened their title defence with a 3-1 success against Bayer Leverkusen last weekend.
The result extended Bayern's impressive record to 14 wins in meetings between these sides, with Bremen picking up their last point against the Bavarians in August 2009.
Germany skipper Manuel Neuer returned between the posts for the visitors - his first appearance since breaking a bone in his foot in April - but was rarely tested.
Bayern started the match on the front foot and almost went ahead during their first attack, but Mats Hummels failed to keep his header down from Joshua Kimmich's corner in the second minute.
The visitors maintained their dominant start and their patient build-up led to Arjen Robben cutting onto his left foot from the right wing but his effort was straight at Bremen goalkeeper Jiri Pavlenka.
The home team were lucky not to concede when Pavlenka failed to deal with a Franck Ribery's corner as the ball fell at the feet of midfielder Corentin Tolisso, but his snap-shot clipped the top of the crossbar from six yards.
Bayern continued to dictate possession but Bremen were dogged in defence and were only tested by long-range efforts from Arturo Vidal before Robben was inches away from breaking the deadlock with a glancing header in the 39th minute.
Ribery forced a great save from Pavlenka just before the break while, at the other end, Max Kruse let fly from the edge of the area but his effort was blocked by Niklas Sule in a rare attack for the hosts as they went into the interval on level terms.
Die Roten started the second half in the same manner as the first but struggled to penetrate the Bremen defence and were nearly caught on the counter-attack, with Hummels recovering just in time to deny Finn Bartels.
The centre-back had a chance at the other end of the pitch when he got on the end of Robben's outswinging corner but his tame header was straight at Pavlenka.
Vidal tested the hands of the Czech goalkeeper with a long-range effort but the hosts continued to threaten on the break with Johannes Eggestein's poor pass spurning another great opportunity with three in support.
And shortly after they found themselves behind as Lewandowski finally broke the deadlock with a deft flick past Pavlenka from substitute Kingsley Coman's driven cross.
Thomas Muller was denied with his first touch by a fine save from the Bremen goalkeeper but Lewandowski soon doubled the away side's advantage with a fine solo goal three minutes later.
Picking up the ball 30 yards out, the striker beat two defenders before firing through the legs of Pavlenka from the edge of the area.
The two goals took the sting out of the Bremen counter-attack and, although Sebastian Rudy and Hummels went close, the visitors saw out the victory.