Bremen, without suspended attacker Diego, failed to replicate Wednesday's German Cup performance when they came from a goal down to beat Borussia Dortmund 2-1.
Bielefeld struck first after 24 minutes when Michael Lamey crossed from the right to striker Artur Wichniarek but after he failed to connect, Thorben Marx was at hand to slot it home.
Bremen, who enjoyed overwhelming possession with a first half share of 73 per cent, equalised when Hugo Almeida unleashed a fierce drive from the edge of the box after combining well with Mesut Ozil and Torsten Frings seconds before the break.
Four minutes after the restart Bielefeld grabbed the winner when Frings lost the ball to Christopher Katongo in midfield and the Zambian fed Wichniarek in the box to fire home.
Elsewhere VfL Bochum scored once in each half to beat Karlsruhe SC 2-0 and lift themselves out of the relegation zone.
Christian Fuchs grabbed the first with an unstoppable drive from 25 metres in the 26th minute before Argentine Diego Klimowicz celebrated his debut by adding the second in the 65th when he rounded keeper Markus Miller in a swift counter attack.
Karlsruhe are a point behind Bochum in 16th on 13 points, ahead of Energie Cottbus on goal difference, and Borussia Moenchengladbach who are bottom on 11 points.
Newcomers Hoffenheim lead the standings with 38 points after beating Cottbus 2-0 on Saturday.
Hertha Berlin climbed to second on 36 points ahead of Hamburg SV on goal difference following their 2-1 win over Eintracht Frankfurt while Bayern Munich dropped to fourth on 35 after losing 1-0 in Hamburg on Friday.
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