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The result keeps Bremen 12th, but they are now 11 points from the relegation places before hosting Bundesliga leaders Bayern on Saturday.
Sargent, 21, put Bremen ahead two minutes after the break in Bielefeld when he guided Milot Rashica's cross over the goalline.
The US international also netted the winner in a 2-1 victory over Eintracht Frankfurt and scored in Sunday's 1-1 draw with Cologne.
With 19 minutes left, Bielefeld replacement defender Nathan de Medina was then sent off for fouling Bremen striker Niclas Fuellkrug.
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The VAR changed the yellow card initially shown to the Belgian defender to a red after reviewing the tackle which crunched into Fuellkrug's Achilles tendon.
Bremen took advantage of the numerical advantage when Maximilian Eggestein cut the ball back from the byline for Kevin Moehwald to score four minutes after the sending off.
The defeat leaves Bielefeld 16th and two points from escaping the bottom three.
A heavy snowfall in Bielefeld meant the match was originally postponed in early March.
ryj/dj