It was an impressive start to the game from the champions, but the opener didn't arrive until the 20th minute, when Philipp Lahm converted from close range after Arjen Robben's cross created chaos inside the Bremen box.
Bremen struggled to prevent the hosts from enjoying complete domination, and they fell further behind midway through the first half when Xabi Alonso found the bottom corner with a free kick which he struck beneath the wall.
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Bayern's creative players were causing problems with every venture forward, and Pep Guardiola's side effectively ended the match as a contest before the break.
Predictably, Bayern remained on top in the early stages of the second half, and were close to scoring a fifth in spectacular fashion when Rafinha's 25-yard strike flew just wide.
Bremen were unable to change the pattern of the contest as the hosts created chance after chance, with Robben somehow firing over after beating the offside trap.
Xherdan Shaqiri came off the bench to help his side continue their dominance with a chipped pass to Lahm, who calmly stroked the ball home for his second of the afternoon.
There was time for Gotze to complete his own brace as he combined with Muller to find space on the edge of the box before capping off an emphatic victory with a powerful strike.