Braunschweig remained bottom of the pile on just 12 points, but it was a solid way to return from the winter break.
The point did little to help Bremen, who are closer to the relegation places than the European spots.
The visitors had the first chance in the game after 19 minutes but Havard Nielsen's header from 12 yards found only the arms of Bremengoalkeeper Raphael Wolf.
Bremen came into the match, Nils Petersen firing their first attempt off target before Zlatko Junuzovic could only shoot wide a minute later after being given time and space 12 yards out.
Eljero Elia then got past Deniz Dogan and passed to Petersen, but the striker found only the side netting from six yards.
Braunschweig were still offering a threat of their own, but again Nielsen headed straight at Wolf.
Bremen went closest to breaking the deadlock three minutes after half-time as Elia fed Philipp Bargfrede, whose fierce shot from 23 yards struck the right post.
The hosts went close again two minutes later, but Omar Elabdellaoui headed Santiago Garcia's header away from the line.
Bremen had a goal ruled out in the 59th minute when Elia's effort was ruled out for offside.
Braunschweig might have snatched the points five minutes later, but Marc Pfitzner's shot went over as both sides had to settle for a share of the spoils.