Robert Lewandowski marked his 100th Bayern Munich appearance with a brace in a 4-0 victory over Mainz.
The Bavarians suffered a surprise defeat to Hoffenheim last week but got back to winning ways in the Bundesliga with minimal fuss and with the lethal Lewandowski at the forefront.
Thomas Muller and Arjen Robben had bagged their first goals of the season in the opening half before Lewandowski added gloss to the scoreline after the interval to mark his milestone appearance in style.
Muller, one of five changes to Bayern's starting line-up from the midweek Champions League win over Anderlecht, swept home first time after some fine build-up play in the 11th minute while Robben was put through on goal and lifted over Rene Adler midway through the first half.
Lewandowski had his first five minutes after half-time when he put the finishing touch to Muller's superb ball across the six-yard area while he was left with an easy header at the far post in the 80th minute to cap an easy three points for Bayern.
Schalke joined Carlo Ancelotti's men on nine points after coming from behind to edge out struggling Werder Bremen 2-1 at the Weserstadion.
Senegal defender Lamine Sane slammed into the net after Ludwig Augustinsson's header had come back off the post in the 20th minute but the visitors levelled almost immediately through Milos Veljkovic's own goal.
It remained that way until eight minutes from time, when a corner was scrambled home by Leon Goretzka, as Bremen were left on one point from their opening four matches.
Philipp Max's goal midway through the first half was followed up by substitute Caiuby's 77th-minute effort as Augsburg claimed a 2-1 win at Eintracht Frankfurt, whose goal from on-loan Benfica forward Luka Jovic proved to be a consolation.
Chadrac Akolo's goal three minutes before half-time gave Stuttgart their second win of the season as they overcame Wolfsburg 1-0.