Leroy Sane and Serge Gnabry dropped to the bench on the side of Bayern, as Benjamin Pavard and Javier Martinez slotted in along with Jamal Musiala who got his full league debut.
Bayern raised eyebrows just before the 20th minute when Lucas Hernandez became the early casualty after making way for Leon Goretzka in an attacking substitution.
The visitors had a good chance to go ahead after four minutes through Leonardo Bittencourt following good work from Milot Rashica, but the former went wide of the right post.
Bayern livened up ten minutes to halftime as Kingsley Coman directed a shot from range way over the top following a combination involving Douglas Costa and Robert Lewandowski.
Maximilian Eggestein handed Bremen a deserved lead on the stroke of halftime after taking on a cutback from Josh Sargent to send a first-time strike past Manuel Neuer.
Bayern went close to the equaliser minutes in the second half when Costa hit the underside of the crossbar following a thumping shot from afar.
The Bavarians drew level inside the closing stages after Coman met a well-weighted cross from Goretzka to plant a perfect header past Bremen goalkeeper Jiri Pavlenka.
Bremen still targeted a turnaround before the closing period, but Bayern equally went on the charge through David Alaba however Pavlenka gathered.
Eric Choupo-Moting had a perfect chance to give Bayern the lead from close-range in the last six minutes, but the Cameroonian went over instead.
Bayern lived dangerously in the closing seconds when Sargent coasted through the left side of the area before getting a shot away, but Neuer parried as it ended 1-1.