It was a really bright start for the away team, who came close on five minutes through Ivan Perisic, but his shot on the turn went just over.
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Then on 13 minutes they did have the goal that they deserved as Kevin de Bruyne rifled the ball from outside the box into the top corner .
Although Stuttgart were hardly in the game they managed an equaliser on 62 minutes through Christian Gentner, who turned the ball into the bottom corner from the middle of the box.
It looked as though it would be enough to earn the hosts a point, but Olic turned in a Vieirinha cross late on to take all three points.