The game's first chance fell to Admir Mehmedi as the midfielder burst down the wing before taking the ball into the box and lashing it towards the Stuttgart goal. However, it was tipped wide.
Vedad Ibisevic then went up the other end to give the away side the lead with a chip over the goalkeeper.
Just seconds later it was 2-0. Timo Werner won the ball straight from the restart and ran into the box before scoring.
Mehmedi had a good chance to reduce the deficit, but was unable to tap the ball in and instead bundled it behind.
Mike Hanke brought them back into the match with a half-volley that crashed into the net, but just four minutes later, Stuttgart completed the win as Werner scored his second of the day with a thumping shot from long range.