The visitors, who hit the woodwork three times, went ahead through Marco Reus in the 19th minute and the Germany international, who is hitting top form ahead of the World Cup after a long injury absence, should have scored again after Mario Goetze sent him through.
But impressive Werder keeper Jiri Pavlenka got his fingers to his shot to deny the winger, who also hit the post.
Instead it was Werder who scored with Thomas Delaney's looping header on the stroke of halftime.
Dortmund hit the woodwork three times in an exciting second half and Pavlenka was on hand with a string of outstanding saves to rescue a point for Werder.
Dortmund stayed third on 55 points, two behind Schalke, who also dropped points in their 1-1 draw with Borussia Moenchengladbach on Saturday. Werder are 12th on 38.
Hoffenheim are fourth on 52 and Bayer Leverkusen a point behind in fifth. The top four teams qualify for next season's Champions League stage.
(Reporting by Karolos Grohmann, editing by Ed Osmond)
