Pierre-Emerick Aubameyang scored twice to give Borussia Dortmund a 2-1 win over Mainz on Saturday.
Aubameyang, who told Bayern Munich striker Robert Lewandowski "the race is started" after his hat trick in Bayern's 6-0 win on Friday, opened the scoring with a header in the 17th minute.
He sealed the result with a penalty in the closing stages, before Yoshinori Muto pulled one back for Mainz in injury time.
Borussia Monchengladbach continued their winning form from DFB-Pokal and Champions League playoff matches by beating Bayer Leverkusen 2-1.
Andre Hahn and Lars Stindl scored for the Foals with Joel Pohjanpalo's first Bundesliga goal not enough for the Werkself.
Alexander Meier scored early and Eintracht Frankfurt held on to defeat Schalke 1-0.
The 13th-minute strike was enough for Frankfurt, who finished with 10 men following Michael Hector's late sending off.
Marcel Risse and Anthony Modeste provided the goals for Cologne, who eased to a 2-0 win at home against Darmstadt to open the season.
Risse tapped in Leonardo Bittencourt's pass before a thunderstorm interrupted the action for 12 minutes in the second half, and Modeste added the second goal just after the hour mark.
Wolfsburg won 2-0 at Augsburg with goals from Daniel Didavi and Richardo Rodriguez.
Didavi scored his first goal for the club by jumping on a loose ball just inside the penalty area in the 35th minute, before Rodriguez's free kick ended matters in the 89th minute,
Hamburg could only draw 1-1 with visiting Ingolstadt despite United States forward Bobby Wood's first Bundesliga goal for the home side.
Wood latched on to a long ball from Hamburg goalkeeper Rene Adler, held off his marker and drilled a low shot past Orjan Nyland.
Ingolstadt equalised with just over 10 minutes of the game remaining when Lukas Hinterseer capitalised on defender Cleber's error.
Information from The Associated Press and Press Association Sport was used in this report.