Monchengladbach went ahead 27 minutes into the match held at Weserstadion with a goal from Germany forward Lars Stindl.
Denmark defender Jannik Vestergaard doubled Monchengladbach's lead just seven minutes later to secure the 2-0 win.
After the win, Monchengladbach are in fifth place, with 14 points, one point behind fourth-place Hoffenheim and two points behind third-place RB Leipzig.
Werder Bremen are in 17th place, with only four points, and remain winless this season.
Borussia Dortmund, who suffered a 3-2 home defeat against Leipzig the previous day, lead the Bundesliga standings with 19 points, just two points ahead of defending champions Bayern Munich.