Hansi Flick's men approached Tuesday's clash at a rain-soaked Weserstadion knowing victory would be enough to retain the crown with two games to spare.
As in Saturday's 2-1 triumph over Borussia Monchengladbach, Bayern were below their best but it mattered not against opposition fighting for their top-flight lives.
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 were 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.