Hofmann came off the bench to play a big part in his side's second goal after they had gone ahead in extra time through Pierre-Emerick Aubameyang's penalty.
"It was difficult to find a way through 1860 Munich sat very deep, especially after the sending-off," Hofmann told the club's official website.
"That's why It took us so long to find a gap. But it was a deserved win. Munich wanted to get to penalties, but we Showed character and kept on trying. That was our biggest strength."
Dortmund return to league action on Saturday with a home clash against Freiburg.