Bellingham, who joined from Birmingham City in July, needed just 30 minutes to open his Dortmund account as he doubled the Bundesliga team's lead after a penalty from Jadon Sancho.
Thorgan Hazard blasted in a free-kick to make it 3-0 when Duisburg defender Dominic Volkmer was sent off for bringing down Erling Haaland.
England Under-21 international Bellingham was withdrawn at half-time before fellow teenager Gio Reyna added a fourth for Dortmund from another set-piece.
Club captain Marco Reus made his first appearance since February following injury, netting within seconds of his introduction on the hour to cap the rout.
Holders Bayern Munich will play fifth tier FC Dueren in mid-October after the Champions League winners were granted extra rest following their triumph in Lisbon.
Schalke's tie against Schweinfurt was postponed after a court ruled the fourth tier side should not be in the competition.