Goals by Alexander Meier in the 52nd and by Stefan Aigner 10 minutes later secured the victory for Frankfurt, which began the season with two defeats. Promoted Braunschweig has lost all three of its games since returning to the Bundesliga after 28 years.
Braunschweig and Stuttgart are bottom of the standings, the only two teams without points three matches into the season.
Halil Altintop connected with a hard cross from the right at the far post to put Augsburg up by one in the sixth minute and Jan-Ingwer Callsen-Bracker doubled the lead in the 36th with a header off another cross.
Vedad Ibisevic converted a penalty in the 42nd for Stuttgart, but Augsburg held on in the second half and Sascha Moelders missed an empty net for Augsburg 10 minutes from time.
Stuttgart’s Ibrahima Traore was sent off in the 70th, six minutes after he had come on as a substitute. It was the eighth red card of the weekend, a Bundesliga record for a match day.
The defeat increases the pressure on Stuttgart coach Bruno Labbadia, with some fans already calling for his ouster.
Stuttgart is also on the verge of missing out on the Europa League after losing 2-1 at Rijeka in Croatia.
In Braunschweig, Meier’s deflected shot from inside the penalty area left goalkeeper Daniel Davari no chance.
Aigner intercepted a poor pass from Omar Elabdellaouim to secure the victory 10 minutes later, easily slipping the ball past Davari from close range.
Frankfurt finished sixth last season when it was promoted and earned a place in Europa League qualifying. It won 2-0 at Qarabag in Azerbaijan in the first leg.
”This has been a successful week for us. We are back on track,” Meier said.
Frankfurt’s coach Armin Veh was pleased.
”We played good football. The team was very present on the field,” Veh said.
Braunschweig hardly threatened Frankfurt’s goal.
”We played with no confidence. That’s my biggest headache. It’s a disappointment, but not such a big disappointment that we should be resigned after only three rounds.”
Defender Deniz Dogan said Braunschweig was still trying to settle down in the top flight.
”We make too many blatant errors. It’s a mental thing as well. It’s early in the season but we should begin to earn some points,” Dogan said.