Bayern moved into a two-goal advantage in the first half, with a superb finish from Arjen Robben being followed up by a stunning David Alaba free-kick, his first league goal of the season.
Max Kruse got one back for Bremen after the break and tensions were raised when the visitors had two penalty claims turned down.
But Carlo Ancelotti's side held on for a record-breaking 13th consecutive league win over Bremen.
In-form Bayern have now won seven straight league matches, while Bremen are winless in four and stay 15th.
Franck Ribery, recalled to the team as one of two changes, had an early shot saved by Felix Wiedwald, before Bremen suffered an early blow when Claudio Pizarro was withdrawn through injury.
The hosts were soaking up pressure but posing a threat on the break, with Serge Gnabry capping one counterattack by testing Manuel Neuer, while Kruse also forced the goalkeeper into action.
But it was the away side who struck first through after 30 minutes, and it was their fearsome wing duo, who have tormented the Bundesliga for almost a decade, that did the damage.
Ribery cut in from the left and drove into the box before squaring for Robben , who fired a magnificent first-time finish high past Wiedwald from just inside the area.
Bayern struck a magnificent second in first-half stoppage-time, Alaba curling in a magnificent free-kick from 20 yards that clipped the post on its way in after Robben had drawn a foul from Niklas Moisander.
Ribery had a goal ruled out for offside after the break, having mistimed his run onto Thomas Muller's pass.
Gnabry fired inches wide after a precise pass from Kruse at the other end, but Bremen did get a goal back eight minutes into the second half.
An impressive move led to Zlatko Junuzovic feeding it into Kruse 's path and he evaded Alaba before thumping a shot past Neuer to net his third goal in six games.
Bayern were denied a penalty when Robert Lewandowski was shoved to the ground by Robert Bauer as he attempted to get on the end of Joshua Kimmich's cross.
Robben was the next to have a claim rejected by referee Sascha Stegemann after he went down under Moisander's challenge in the box.
Muller and Robben were replaced by Renato Sanches and the returning Kingsley Coman as he looked for a goal that would make sure of victory, but Bremen were still battling, Kruse lashing just over from a difficult angle.
The hosts, though, could not fashion a clear late opportunity for an equaliser as Bayern held on to keep their winning run alive.