The 19-year-old opened the scoring on 12 minutes before Klaas-Jan Huntelaar doubled the home side's advantage towards the end of the opening period.
Robert Lewandowski pulled a goal back in the second half but the damage had already been done, with S04 moving into the top four to leave Draxler overwhelmed with emotion.
"The adrenalin was really flowing. I didn't know how to handle my emotions - I think you could see that," he told Bundesliga.com. "I think we were really, really good in the first 45 minutes. We didn't give Dortmund room to breathe.
"Everything really came together: my 100th appearance, my first derby win and a derby goal to boot. It doesn't get much better for a Schalke player than that."
The midfielder now has seven league goals to his name this season, including three in his last two games and the teenager admitted he was glad to be adding an end product to his game.
"I want to score goals," he said. "I said that a few weeks ago. I could still do with another 15, but I'm really pleased to have scored three in the last two games!
"Now I've got seven this season and would really like to make it into double figures. I've always said I carry more of a goal threat playing as a No.10 rather than on the left, but I don't just measure myself by goals. At the end of the day, it's about Schalke finishing the season in the European places."
The Gelsenkirchen club now turns its attention to the Champions League where the club faces Galatasaray in the second-leg of their last 16 clash on Tuesday, after a 1-1 draw in the first leg.