The result left Cologne in sixth place with two games left in the season.
Cologne were 2-0 by the 28th minute, having enjoyed an explosive start with French striker Modeste and Leonardo Bittencourt on target.
Werder, who had won nine of their last 11 matches as they climbed out of the relegation spots and into European contention, did not take long to draw level with goals from Fin Bartels and Theodor Gebre Selassie.
Simon Zoller's chip over the keeper on the stroke of halftime kept Cologne a goal ahead and they scored another minutes after the restart with Modeste's close-range effort for his 25th league goal.
The hosts then had to endure a nerve-wracking second half after substitute Serge Gnabry pulled a goal back for the visitors, who were desperately pushing for yet another equaliser.
Cologne are on 45 points, ahead of Werder on goal difference. Freiburg, in eighth on 44, take on Schalke 04 on Sunday. Sixth place guarantees a spot in the Europa League group stage with the seventh-placed team heading into the competition's qualifiers.
Bayern, who have already secured the title, take on last-placed Darmstadt 98 on Saturday. Fourth-placed Borussia Dortmund (57 points) host third-placed Hoffenheim (68) as both teams seek a spot in next season's Champions League group stage.
(Reporting by Karolos Grohmann, editing by Pritha Sarkar)
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