Gladbach, looking for their first home win since January, hit the woodwork in the first half and went ahead in the 49th with Florian Neuhaus.
But Davy Klaassen was left unmarked in the 79th to level for the visitors, who remain unbeaten in 2019.
Gladbach have now managed just one win in their last eight league games, and are fifth on 48 points, with Eintracht Frankfurt in fourth on 52 with six games left.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
Werder, who have now scored in each of their last 29 league matches, dropped to eighth on 43.
The top four teams advance to next season's lucrative Champions League group stage.
Champions Bayern Munich returned to top spot after demolishing Borussia Dortmund 5-0 on Saturday to move a point clear of their title rivals.
(Reporting by Karolos Grohmann; editing by Clare Fallon)
