Pep Guardiola’s side made it three wins in seven days, scoring 14 goals and conceding just one, as they not only padded their lead in the domestic flight but also qualified for the Champions League quarter-finals.
German international striker Thomas Mueller grabbed his fifth goal in a week with a left foot shot past Raphael Wolf to put the champions 1-0 in front on 24 minutes at the Weser-Stadion.
Austrian defender David Alaba then scored his second league goal of the season to cushion the advantage.
Polish international Robert Lewandowski added the gloss with two late goals to round out the scoring.
Guardiola was evidently delighted with a fine week at the office.
“The team maintained total concentration throughout and did very, very well,” said the Spaniard.
“After the match against Donetsk it wasn’t easy adapting to new opponents but it was one of those days when I’m so proud to be coach of this team.”
While Bremen, who came into the weekend five points behind the European places, toiled bravely they were unable to breach the goalline of Pepe Reina, who was standing in for first-choice ‘keeper Manuel Neuer.
The absence of Arjen Robben and Franck Ribery, who picked up knocks during the 7-0 rout of Shakhtar Donetsk in teh Champions League on Wednesday, had little effect as Bayern picked up their 20th victory in 25 league outings against just one defeat.
Another player who got a chance to shine was former Germany captain Philipp Lahm who came on as a substitute for the final ten minutes for the first time since fracturing his ankle in mid-November.
“It was great to be back out on the pitch after such a long time away. Many thanks to the team, because I think if it had been tighter I wouldn’t have had the chance to come on,” said Lahm.
Elsewhere, Eintracht Frankfurt consolidated their place in the upper half of the table with a routine 4-0 win over third-from-bottom Paderborn.
Alexander Meier got the home side on track with a goal after 27 minutes before Marc Stendera, Stefan Aigner and Nelson Haedo Valdez also got on the scoresheet in a feisty afternoon encounter that featured eight yellow cards.
Mainz picked up a crucial 2-0 victory over Augsburg, thanks to a distinctive Asian flavour, as they eased their relegation fears.
Shinji Okazaki added to his record as the highest Japanese scorer in Bundesliga history, with the opener on 32 minutes, before former South Korea captain Koo Ja-cheol guaranteed the points in the final minute.
Hertha Berlin missed the chance for three valuable points as they were deprived victory in the final minute by a Joel Matip equaliser for Schalke.
A see-saw match finished 2-2 in the capital.
Eugen Polankski struck either side of half-time for Hoffenheim as they boosted their European ambitions for next season with a 3-0 home win over 10-man Hamburg.
Jaroslav Drobny conceded the penalty that led to a straight red card and Polanski’s opener before the 28-year-old Polish midfielder helped seal the win with his second eight minutes from time.
Sebastian Rudy added a third to the delight of the home fans in the dying minutes.
On Friday, Bayer Leverkusen cantered to a 4-0 win over Stuttgart and climbed to third place ahead of idle Borussia Moenchengladbach.
In the final match on Saturday, resurgent Borussia Dortmund are at home to Cologne, ahead of their Champions League tie against Juventus on Wednesday, while on Sunday, Europa League hopefuls Wolfsburg await second-from-bottom Freiburg.
Finally, Moenchengladbach host Hanover in the ultimate match of the weekend.