Delaney provided an assist for Christian Pulisic to give Dortmund the lead and, following Oliver Fink's equaliser courtesy of a Marwin Hitz howler, restored their advantage before Mario Gotze poached a third.
Dusseldorf midfielder Adam Bodzek was sent off and Dawid Kownacki pulled one back late on as Dortmund edged a result which, coupled with Bayern's goalless draw with RB Leipzig, ensures the title race goes down to the wire with Dortmund two points behind their bitter rivals ahead of their last day trip to Borussia Monchengladbach.
A point should be enough for Bayern to clinch the title as they take on Eintracht Frankfurt at home, but Dortmund look determined to give themselves every chance of capitalising if the champions slip up.