Dutch international Wout Weghorst headed home for the winning goal with the remaining eight minutes to raise his side to sixth place and place in the Europa League qualifier, 12th place of the season.
By contrast, Florian Kohfeldt is in second place from the bottom, six points from automatic safety and three playoff spots, with just four games.
Since the founding of the Bundesliga in 1963, Werder has been in Germany’s top flight for 55 years, and it wasn’t until 1980 that he was knocked out before rebounding straight the following season.
But the double winners in the 2003/04 season have struggled in recent years and form has been poor since the re-launch of the current campaign, losing two straight home matches.
A visit to the lower flank of Paderborn next weekend and a clash with relegation rival Mainz could prove crucial, but Werder must also face Bayern in Munich in two weeks in a match in which Bayern could seal the eighth straight Bundesliga crown.
“The last two defeats at home have been very disappointing. We have to win next week. We will fight to the end,” Werder captain Niklas Moisander said on the club’s social media page.
Before the start, both teams gathered around the center circle at Weser Stadium before getting down on one knee, repeating gestures made by Borussia Dortmund and Hertha Berlin players on Saturday.
A later 1-1 home draw for Union Berlin against Schalke helped Werder hard.
Union was a tough favorite that should have been knocked out before the start of the season, but pulled seven points away from Werder, with a precious draw in the capital.
Schalke reached opener Robert Andrich in the 11th minute with just one point out of 15 since the restart of the Bundesliga, but at least scored a point in the 28th minute of a goal from Jonjoe Kenny, who was on loan from English Premier League Everton.
Repeating the pre-premiere procedures in an earlier game, both teams also rose to their knees in a gesture against racism first made by NFL player Colin Kaepernick in 2016.
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