Karim Bellarabi set up Julian Brandt to fire the visitors ahead with just 11 minutes played, and Stefan Kiessling came close to a second before half-time for Roger Schmidt's side.
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Bundesliga: Stuttgart 0 Bayer Leverkusen 2
Bayer Leverkusen moved to within two points of the Champions League places with a 2-0 win over Stuttgart on Sunday.
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But Brandt turned provider for Bellarabi after the break to settle the match, teeing up the right??winger to slot past Przemyslaw Tyton.
Stuttgart fought for a foothold but were unable to keep Leverkusen under any significant pressure, meaning they remain 11th in the Bundesliga table.
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