The early danger signs were there for Augsburg, as Deniz Undav forced Finn Dahmen to tip the ball over his crossbar in just the third minute, but the home side didn’t heed the warning.
Shortly before the quarter-hour mark, Angelo Stiller’s cross from the left was batted down by Dahmen straight to Undav, who tucked away his 17th league goal of the season.
The hosts looked to have quelled the early Stuttgart pressure when Elvis Rexhbecaj had an effort on goal midway through the half, yet that was just a precursor to more dominance from the visitors.
With a little less than 30 minutes on the clock, a poor clearance was played back into the danger area by Chema Andres, whose header landed perfectly for Nikolas Nartey to backheel for Tiago Tomas to sweep home.
With their very next attack, Die Schwaben were almost out of sight, as Nartey finished himself when he got ahead of his marker to turn home Maximilian Mittelstadt’s low cross.
Matters nearly got worse for Augsburg before the break when the referee blew for a penalty against Han-Noah Massengo, only for VAR to deem he hadn’t done enough to give away a penalty when impeding former Burnley teammate Lorenz Assignon.
Unsurprisingly, Manuel Baum made a triple change at the break, which ushered in a positive 15 minutes for his team. First, Massengo tested Alexander Nubel from distance, and Cedric Zesiger skied a great chance from close range following a free-kick, before the Fuggerstadter cut the deficit to two. Robin Fellhauer found space on the right and his square ball fed Alexis Claude-Maurice, who had two efforts blocked before the arriving Fabian Rieder powered in the rebound.
However, hopes of a comeback lasted mere seconds as Stuttgart scored almost straight from the kick-off. A ball over the top found Chris Fuhrich, who cut inside and saw his effort saved by Dahmen, only for Undav to react the quickest and complete his brace.
In the final 20 minutes, the hosts displayed their fighting spirit when a drilled Dimitris Giannoulis cross was taken down by Kristijan Jakic and, while his effort was denied by Nübel, Anton Kade followed up to score. But Stuttgart were finally out of sight seven minutes from time when Undav selflessly drew the goalkeeper and pulled the ball back for Ermedin Demirovic to add a fifth.
That sealed a first away success in four for Sebastian Hoeness’ side as they bounced back quickly from their midweek UEFA Europa League exit. Meanwhile, this is a third straight defeat for Augsburg and, after nine losses and a draw in their last 10 H2Hs, Augsburg will be happy to see the back of their opponents here.