A slow start from the hosts was perhaps to be expected after they were taken all the way to extra-time on Thursday as they booked their place in a second successive DFB-Pokal final.
Bremen threatened to upset the odds and break the deadlock early, but Senne Lynen – who has never scored in 92 Bundesliga appearances – failed with two efforts before Jens Stage looped a header wide of the far post.
Stuttgart failed to heed those warnings, and on 18 minutes, they could have little complaints at falling behind to the in-form Stage, who swept home a gorgeous first-time low finish from Yukinari Sugawara’s cutback.
Bremen goalkeeper Mio Backhaus was busy in response, keeping out a powerful Bilal El Khannouss header before gathering Maximilian Mittelstadt’s deflected free-kick.
His most impressive work came in stoppage time to deny a curling Deniz Undav effort, moments after Jovan Milosevic squandered a big chance to double Bremen’s advantage when he curled wide after flooring Dan-Axel Zagadou.
Die Schwaben showed few signs of improvement in the second half’s early stages, prompting Sebastian Hoeneß to introduce Chris Fuhrich and Ermedin Demirovic from the bench.
That proved a masterstroke, as within four minutes of his introduction, Demirovic headed in El Khannouss’ delivery to restore parity.
Die Werderaner’s attacking threat had largely disappeared since the restart, yet a huge chance to move back ahead passed them by when Stage could only tamely shoot straight at Alexander Nubel after being left unmarked inside the six-yard box.
At the other end, Backhaus parried Angelo Stiller’s free-kick away from danger as Bremen held on for a draw that sees them leapfrog three of their relegation rivals in the Bundesliga and lifts them six points clear of the bottom three.
This represents their first point of the campaign against the current top five, while Stuttgart have now failed to win three of their last four league outings.