Brazilian playmaker Diego put the hosts ahead early in the first-half before Pierre Wome doubled the lead in the 34th minute.
Roy Makaay pulled one back for Bayern three minutes later but an own goal by Brazilian defender Lucio sealed the victory for Bremen.
Egyptian striker Mohamed Zidan didn't take part in the game as Bremen's Austrian coach Thomas Schaaf opted to leave him on the bench.
Bremen are in charge of the league table with 16 points, ahead of second-placed Schalke on goal difference.
Diego broke the deadlock in the 11th minute when he latched on to Torsten Frings' through pass and span around the marking defender before firing into the roof of the net.
Cameroonian full-back Wome added the second after he unleashed a powerful free-kick that took a deflection off Lucio and went past Bayern keeper Oliver Kahn.
Dutch striker Makaay narrowed the gap three minutes later with a brilliant left-footed volley home after being set-up by Claudio Pizarro.
Lucio converted Wome's cross into his own net two minutes past the hour mark to ensure the win for Bremen.
Elsewhere, two first-half goals from Zlatan Bajramovic and Levan Kobiashvili gave Schalke a 2-1 home win over Hannover.
Jan Rosenthal scored the consolation for Hannover seven minutes after the break.
نرشح لكم
كأس العالم - مودريتش: أستمتع بكل لحظة لأن النهاية تقترب
كأس العالم - خاميس: رونالدو صديق عزيز وقدوة للجميع
كأس العالم - 6 تصديات.. ديوجو كوستا رجل مباراة البرتغال ضد كولومبيا
رونالدو يبتعد عن ميسي
كأس العالم - أول الراحلين بعد نهاية المشوار.. استقالة كلارك من تدريب اسكتلندا
كأس العالم - نيكو ويليامز: أسوأ أيام حياتي.. تعرضت لإصابة جديدة بعد عام عصيب
انتهت كأس العالم - كولومبيا (0)-(0) البرتغال.. تعادل سلبي
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