Steven Zuber fired Stuttgart ahead after 61 seconds. The former Hoffenheim striker stayed cool after he was sent through by Mario Gomez to shoot beyond Bremen keeper Jiri Pavlenka and inside the far post.
Despite more possession for the hosts, it was Stuttgart which had the better chances - Gomez spurning two good opportunities - and the visitors were left to rue the misses when Max Kruse set up Dutch midfielder Davy Klaassen to equalize with a powerful strike before the break.
"I'm sorry for the team," Gomez said. Bremen brought on Claudio Pizarro, who became the oldest ever goalscorer when he grabbed a late equalizer against Hertha Berlin last weekend, for the last half-hour but the 40-year-old Peruvian could not find the winner.
American forward Josh Sargent made his first league start for Bremen. Stuttgart remained in the relegation zone with 16 points from 23 games. On Saturday, second-place Bayern Munich hosts Hertha. Leader Borussia Dortmund takes on Bayer Leverkusen on Sunday.
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