Goals from Sebastian Prodl and Fin Bartels either side of half time earned Bremen their second successive win and sent German giants Borussia Dortmund bottom.
Zlatko Junuzovic had two early efforts for the hosts at Weserstadion, firstly shooting wide from 25 yards. His next effort was on target, but Stuttgart keeper Thorsten Kirschbaum made a comfortable save.
It was Armin Veh's side who came closest to opening the scoring before the half-hour mark as Martin Harnik was released into the box by Sercan Sararer, only to stumble on the ball and be crowded out by Bremen defenders.
Bremen were ahead nine minutes later as Prodl's header from a corner was deflected past Kirschbaum.
Stuttgart replied strongly and could have equalised prior to the interval, as Christian Genter headed wide from close range, Alexandru Maxim shot high from the edge of the box and Raphael Wolf saved from Harnik.
They knocked on the door again three minutes after the restart as Antonio Rudiger poked just wide following Genter's knockdown, but Bremen soon doubled their advantage against the run of play.
Again it was a corner which was the source as Bartels met Junuzovic's delivery at the near post to guide home.
The second goal was a killer blow to Stuttgart and Werder looked the most likely to add to the scores before the final whistle as Franco Di Santo squandered several chances to add his name to the scoresheet.
Two was enough for Bremen to continue their 100% record under new manager Viktor Skrypnyk and climb to 15th, while Stuttgart are only propped up by Dortmund following a sixth defeat of the season.