Borussia MG saw off VfB Stuttgart 3-1, while TSG Hoffenheim dispatched FC Augsburg by the same margin in Saturday's Bundesliga action on Saturday.
Bayern München maintained their place atop the Bundesliga table with a comfortable 3-0 win over Mainz 05 on Saturday night.
The in-form Robert Lewandowski netted a second-half brace before Kingsley Coman added a third to see the Bavarians claim their seventh win in as many games to start the new campaign.
Last season's runners-up VfL Wolfsburg lost further ground on the defending champions as they were held to a 1-1 draw with Hannover 96 at the Volkswagen Arena.
Bas Dost gave the hosts the lead just before half-time but Hiroshi Kiyotake's superb strike saw Hannover secure a well-deserved draw against last season's DF Pokal winners.
Granit Xhaka, Christian Gentner and Raffael all got on the scoresheet as Borussia MG eased past VfB Stuttgart 3-1, who grabbed a consolation through Daniel Ginczek's penalty.
Elsewhere, TSG Hoffenhiem claimed a 3-1 win over FC Augsburg courtesy of a Kevin Holland brace and a late Jonathan Schmid goal. Ja-Cheol Koo got the goal for Augsburg.
Leverkusen, meanwhile, thrashed Bremen 3-0 at the Weserstadion to maintain their solid start to the campaign, Kevin Kampl, Admir Meehmedi and Julian Brandt all getting on the scoresheet.
In the night's final fixture, Leroy Sane scored the only goal of the game as Schalke 04 grabbed a narrow 1-0 win over Hamburger SV in a tightly contested affair at the Volksparkstadion.
Saturday's Bundesliga results
VfL Wolfsburg 1-1 Hannover 96
VfB Stuttgart 1-3 Borussia MG
FC Augsburg 1-3 TSG Hoffenheim
Bremen 0-3 Leverkusen
Mainz 05 0-3 Bayern München
Hamburger SV 0-1 Schalke 04