Peniel Mlapa gave Monchengladbach the lead in the 72nd minute but Aleksandar Ignjovski equalised for the visitors just five minutes later.
The draw left Gladbach in eighth place and Bremen, who at least snapped a three-game losing streak - in 13th spot and eight points above the relegation play-off berth.
The hosts looked to have opened the scoring from their first chance after 15 minutes, when Patrick Herrmann's effort from Luuk de Jong's through-ball was initially allowed to stand. But, after consulting with his assistant, the referee disallowed the goal for offside.
Bremen went close 11 minutes later, Nils Petersen's 12-yard blast from Kevin De Bruyne's flying inches wide.
Petersen threatened again with 17 minutes gone, but Gladbach goalkeeper Marc-Andre ter Stegen fended his shot from just outside the area around the left post.
Gladbach mustered another chance in first-half stoppage time as Amin Younes played a fine ball forward to Herrmann, but he lashed over the bar.
Ter Stegen was called into action again midway through the second half to keep out a De Bruyne shot following a solo run from the Belgium international.
The deadlock was finally broken by Gladbach soon after, Mlapa heading home Oscar Wendt's corner.
The lead lasted only five minutes, however, before De Bruyne crossed for Ignjovski to fire home.
Gladbach passed up a golden opportunity to clinch all three points in the 90th minute as Bremen goalkeeper Sebastian Mielitz slowed Mlapa enough to allow defender Mateo Pavlovic to get in the way of the shot.