Dortmund were able to take the lead in minute 21 with a stunning header.
After recovering the ball just outside their own half, Dortmund were able to drive down the left wing.
Delaney provided a stinging cross, perfectly placed to meet Dahoud, who was practically unmarked in the centre.
Dahoud flew like a salmon into the air, and headed a bullet past Gulacsi in the Leipzig goal.
The header marked his first professional goal for the BVB.