Bayern winger Arjen Robben notched his 12th league goal this season when he picked up the ball just inside the box and drilled in an unstoppable left-foot shot in the 41st minute for the visitors.
Stuttgart, who hit the post in the first half, went further behind in the 51st minute when David Alaba curled a spectacular 35-metre free kick into the top corner of the net.
"We are not perfect. We can still improve," Bayern coach Pep Guardiola told reporters. "We should run less and move more with the ball in our possession."
Bayern, who had claimed one point from their previous two games, move up to 49 points with Stuttgart, champions in 2007, dropping to last place on 18.
"That goal just before the break was crucial," Robben said. "Stuttgart defended in numbers and it was good that one went in. It was about time we got three points from a game."
Belgium winger Kevin De Bruyne scored twice for second-placed VfL Wolfsburg in their 3-0 win over Hoffenheim, taking his tally to four goals in three matches and keeping his team eight points behind Bayern.
SCHUERRLE SHINES
Andre Schuerrle, Wolfsburg's record signing from Chelsea, made his first start and set up Bas Dost for the opening goal.
The 2014 World Cup winner also crashed the ball against the bar in the 28th minute and De Bruyne pounced on the rebound to make it 2-0.
Last season's runners-up Dortmund breathed a huge sigh of relief after beating Freiburg in their relegation battle, their first victory since early December lifting them to third from bottom.
Marco Reus gave attacking Dortmund a morale-boosting early lead before Pierre-Emerick Aubameyang struck twice.
The Gabon international capped a quick break with a fine run and shot for his opener. He then scored again after a dizzying passing move in the Freiburg box in the 72nd minute.
"We saw what happens if you have self-confidence," said coach Juergen Klopp whose Dortmund team meet Juventus in the Champions League last 16 later this month.
"Today things were a lot better. I am not surprised. I know what this team is capable of."
Coach Pal Dardai enjoyed a winning debut at Hertha Berlin with a 2-0 victory over 10-man Mainz 05. He replaced the sacked Jos Luhukay on Thursday.
(Reporting by Karolos Grohmann, editing by Tony Jimenez)
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