RB Leipzig forward Jean-Kevin Augustin gave his side an early 1-0 lead on Monday after opening the scoring in the first minute.
However, Dortmund fought back to score the equalizer with its midfielder Mahmoud Dahoud netting the goal 20 minutes later.
Just five minutes before the end of the first half, Leipzig midfielder Marcel Sabitzer scored an own goal to give a 2-1 lead for Dortmund.
Midfielder Axel Witsel netted the third goal three minutes later to end the first half with a 3-1 lead for Dortmund.
Dortmund forward Marco Reus sealed the home win with the fourth goal in stoppage time.
That goal was the 100th career tally for Reus, according to Borussia Dortmund’s official Twitter account.
With this win, Dortmund leads the Bundesliga table with three points on goal difference ahead of Bayern Munich, which kicked off its title defence run with a 3-1 home win over Hoffenheim on Friday.
Leipzig is now at the bottom of the table with no points after the end of the first round.
Earlier on Sunday, Mainz 05 forward Anthony Ujah scored the winner to help his side earn a 1-0 home victory over VfB Stuttgart in the same round.
With 14 minutes to go, Ujah netted the winning goal to secure the first three points for Mainz this season.
Mainz holds the eighth position with three points, while Stuttgart is in the 14th spot with no points. >