Kai Havertz's second-half winner earned Bayer Leverkusen their first Bundesliga points of the season as they beat Mainz 1-0.
Bayern Munich made it three wins from three under Niko Kovac in the Bundesliga with a 3-1 victory over Bayer Leverkusen.
Leon Goretzka scored his first goal for Bayern Munich as the defending Bundesliga champions won 3-0 at Stuttgart.
Borussia Dortmund recovered from the shock of conceding a goal in the opening minute of the new Bundesliga season to beat RB Leipzig 4-1.
Schalke consolidated second spot and guaranteed their Champions League place for next season with a 2-1 triumph at Augsburg.
Borussia Dortmund missed the chance to go second in the Bundesliga as they drew 1-1 at Werder Bremen.
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