Georg Niedermeier gave Stuttgart the lead after 55 minutes before Aaron Hunt scored the equaliser for the home side in the 79th minute.
Bremen increased their unbeaten run to five matches to improve to 29 points, while Stuttgart and new coach Huub Stevens picked up their second-straight draw after an eight-match losing streak, moving up to 21 points.
The first half-hour lack any real highlights until the first chance after 32 minutes as Luca Caldirola crossed into the box but Franco Di Santo shot just over the framework.
Stuttgart were awarded a penalty in the 45th minute as Assani Lukimya was ruled to have handled Gotoku Sakai's shot. Martin Harnik stepped up to take the penalty against his old team but watched his shot glance off the outside of the right post to keep it at 0-0.
Bremen had a chance to pull ahead in the 53rd minute but Stuttgart keeper Sven Ulreich did a good job holding a blast by Aleksandar Ignjovski.
Lukimya saved a goal a minute later, stopping at the line a shot by Harnik after the Austrian international had got past three defenders.
But Stuttgart grabbed the lead after 55 minutes as Konstantin Rausch sent a high ball over the defence to Niedermeier, whose header was stopped by Bremen keeper Raphael Wolf but who was quicker to the loose ball and beat Wolf with the rebound.
The guests had a chance to double the advantage after 67 minutes but Sakai shot over the bar from 10 yards out.
Bremen equalised with 11 minutes left on a set-piece with Hunt placing his free-kick from 19 yards out directly into the open corner.