Jakub Blaszczykowski's goal just before the break looked enough for lacklustre Dortmund but Stefan Reisinger equalised in the 78th minute for the battling visitors to snap the champions' three-game winning streak.
Dortmund, who take on Bayern in the big match of the season on Saturday, lacked speed and precision inside the box with playmaker Mario Gotze and central defender Mats Hummels rested.
"We did not put them under enough pressure," Dortmund coach Jurgen Klopp told reporters. "We were not clear enough although to be honest we did not have that many chances. Dusseldorf played good counter-attacks."
Dortmund, desperate to close in on Bayern ahead of Saturday's game, had to wait until two minutes from half-time to crack open a populous Fortuna defence.
Poland captain 'Kuba' Blaszczykowski drilled in a superb volley after a lightning quick combination with Kevin Grosskreutz in the box.
Fortuna were unlucky not to score when Reisinger's drive from 10 metres was accidentally blocked by his team-mate Ken Ilso with Dortmund keeper Roman Weidenfeller beaten.
Reisinger was not to be denied, however, shaking off Marcel Schmelzer to head in through Weidenfeller's legs at the far post in the 80th minute.
Dutch striker Klaas-Jan Huntelaar scored on the rebound after Rene Adler did well to save his spot kick with 10 minutes to go but it was the hosts who struck again with Milan Badelj converting his penalty in the final minute to see Hamburg bounce back from last week's defeat to Fortuna.
