Hansi Flick's men approached the clash at a rain-soaked Weserstadion knowing victory would be enough to retain the crown with two games to spare.
As in the weekend's 2-1 triumph over Borussia Monchengladbach, Bayern was below its best but it mattered not against opposition fighting for its top-flight life.
Robert Lewandowski's sublime 43rd-minute finish proved enough to seal points and the championship, his 31st goal of the league campaign wrapping up a 30th German title despite Alphonso Davies being sent off for a second bookable offence 11 minutes from time.
Bayern was sluggish out of the blocks and lacked their usual fluency, the visitors fortunate to see Maximilian Eggestein's low drive from the edge of the area flash wide of the left-hand post.
Flick's side enjoyed predictable dominance of possession but it did not tell until the 43rd minute, when Lewandowski produced a lethal demonstration of his finishing prowess.
Lewandowski chested Jerome Boateng's ball in from the right and fired a right-footed effort beyond Jiri Pavlenka to surpass 30 goals in a Bundesliga season for the first time in his career.
The Poland international had the ball in the net again within 10 minutes of the second-half restart but the flag was correctly raised after Thomas Muller strayed offside in the build-up.
Davies was dismissed for a foul on Milos Veljkovic before Pavlenka was forced into action to prevent Kingsley Coman from making the game safe, with Manuel Neuer producing heroics at the other end, his fingertip save denying Yuya Osako a dramatic late leveller.