The meeting, held in Dortmund, ended with a score of 2: 0 in favor of the home team.
Borussia's victory was brought by a goal from Jadon Sancho, who converted a penalty in the 78th minute, and Erling Holland, who scored in extra time by the second half.
In the third round, Zenit will host the Roman Lazio at home, while Borussia will play away with the Belgian Brugge.
Earlier it was reported that Krasnodar lost to Chelsea in the Champions League.