Ciprian Marica put the home team in front after 10 minutes and two goals from Cacau gave Stuttgart a 3-0 lead at the interval after Torsten Frings missed a penalty.
Cacau also missed a penalty before Christian Gentner added a fourth and Georg Niedermeier a fifth.
Arthur Boka then sealed the rout as Stuttgart lifted themselves out of the danger zone and piled the pressure on Bremen coach Thomas Schaaf.
If this is what happens after playing in the Europa League on a Thursday night, Stuttgart will be asking for more European fixtures in future.
The Swabians demolished Borussia Monchengladbach 7-0 just 48 hours after beating Young Boys in Europe and they defeated St Pauli after a win over Getafe.
They had been Stuttgart's only two wins of the season so far in the Bundesliga and, having destroyed Getafe 3-0 in midweek, they notched win number three of the season in style.
Marica put the home team in front after just 10 minutes with a low shot past Tim Wiese after Timo Gebhart had led the ball forward unchallenged from the midfield.
Marica almost made it 2-0 moments later, but Wiese did not want to be beaten this time.
Bremen missed a chance to get back in the game in the 24th minute when Sven Ulreich saved Frings' penalty after the Stuttgart goalkeeper had brought Aaron Hunt down inside the area.
The rest of the game belonged to Stuttgart with Cacau doubling their lead after half an hour, converting a cross from Marica.
The Germany international made it 3-0 just before the break with a simple tap-in from Timo Gebhart's pass.
Cacau missed the chance to complete a hat-trick after an hour when his penalty was saved by Wiese.
Gentner added the fourth goal in the 68th minute, shooting across Wiese into the far corner before Niedermeier scored the fifth with a header from Marica's cross.
There was time for Boka to add a sixth, stroking the ball inside Wiese's near post to condemn Bremen to their fourth straight defeat.