Poland international Robert Lewandowski scored the decisive goal on the cusp of half-time after chesting down Jerome Boateng’s chip over the Bremen defence and volleying past Bremen goalkeeper Jiri Pavlenka. It was the 31-year-old's 31st Bundesliga goal of the season.
The victory came under threat though in the last 20 minutes of the game after Bayern defender Alphonso Davies was sent off for two bookable offences.
But Bremen were unable to capitalise on their numerical advantage to salvage at least a draw.
Bremen’s defeat leaves them 17th in the 18 team division on 28 points. They are three points from the safety of 15th place.
Bayern’s victory at the Wohninvest Weser-Stadion took them onto 76 points from their 32 games. Borussia Dortmund, who host Mainz on Wednesday night, can only amass 75 points from their remaining three fixtures.
Former Bayern midfielder Bastian Schweinsteiger, who played in the side for the first three titles, was among the first to salute Hansi Flick's men.
"Wonderful memories of the first three," said the 35-year-old on Twitter.
Jawoll! Glückwunsch zur 8. Meisterschaft in Folge, @FCBayern! Großartige Erinnerungen an die ersten drei 😉 #MiaSanMia pic.twitter.com/LoZ5WBW9eH
— Basti Schweinsteiger (@BSchweinsteiger) June 16, 2020
As Bayern were notching g up a record-extending 30th German title, Arminia Bielefeld were celebrating their return to the top flight for the first time since 2009.
They claimed one of the two automatic promotion places from the second division after Hamburg drew 1-1 with Vfl Osnabruck.
Hamburg, who have 54 points from their 32 games, face a fight for second with Stuttgart and Heidenheim.
Stuttgart can leapfrog Hamburg on Wednesday night if they beat Sandhausen.
