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Second-placed Leipzig moved within a point of Bayern, who play Stuttgart on Saturday, and next face the reigning champions in the league on April 3.
A draw with Champions League-chasing Eintracht Frankfurt last time out had seen Leipzig slip to four points off the pace.
But Julian Nagelsmann's men dominated against relegation-threatened Bielefeld from the start.
Arminia goalkeeper Stefan Ortega made an excellent early save from Emil Forsberg, before Marcel Halstenberg headed over just after the half-hour mark.
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Forward Christopher Nkunku almost grabbed the opening goal shortly before the interval, but his effort was tipped onto the bar by Ortega.
The dogged hosts were broken down less than a minute into the second half, though, as Dani Olmo got in behind and squared the ball for Sabitzer to net a simple tap-in.
It was one-way traffic as Leipzig enjoyed 75 percent of possession and Bielefeld failed to muster a shot on target, and Ortega had to be alert again to prevent Nkunku adding gloss to the scoreline.
Bielefeld remain one point and one place above the relegation play-off spot, currently occupied by Hertha Berlin.
jc/bsp