Two goals from Pierre-Emerick Aubameyang – once of Milan and linked with a return to his former club – and a strike from Nuri Sahin were enough to hand Dortmund victory.
Carlos Bacca scored the consolation Milan goal.
Sahin opened the scoring with a low drive before Aubameyang doubled Dortmund’s lead from the penalty spot. Bacca pulled one back to spark hopes of a fightback. Aubameyang poured cold water over those hopes in the second half.
The wet conditions created problems for both goalkeepers and Marco Storari should have saved Sahin’s effort.