The meeting, which took place at Giuseppe Meazza, ended with a score of 2: 2.
Inter scored first.
On the 49th minute Romelu Lukaku scored.
Borussia responded with goals from Rami Bensebaini, who converted a penalty in the 63rd minute, and Jonas Hoffman, who scored in the 84th minute.
The second goal of Lukaku, who scored in the 90th minute, helped the Nerazzurri escape the defeat.
In the second round, Inter will play away with Ukrainian Shakhtar, while Borussia will host Real Madrid at home.
Earlier it was reported that Koman's double helped Bayern to defeat Atlético in the Champions League.