And the forward admitted it was a night he will not forget in a long time.
"I really enjoyed it," Reus said. "I had goosebumps and I don't think there is much more to say than that.
"Of course I had dreamed of scoring on my debut and that was very important for me, but it was more important for the team."
After Reus' 11th-minute opener, Dortmund appeared to struggle against a well-organised young Bremen side, which equalised through
"I don't think anybody can expect us to be at our very best from the beginning," added Reus on his club's website.
"We saw that we still have a great deal of work ahead of us, but it was important that we won the game."
"We have dropped some points here," he said. "We are frustrated about that.
"We played a good game and unfortunately we were unable to take something away, and that is a big shame."