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 Goetze and central defender Mats Hummels rested.
Fortuna were down to 10 men in the final minutes after a second booking for Ivan Paurevic.
The draw lifted Dortmund to 26 points, two clear of Schalke 04 who lost 3-1 at Hamburg SV and Eintracht Frankfurt, beaten 3-1 by visitors Mainz 05.
Bayern, top on 34, travel to Freiburg on Wednesday and Bayer Leverkusen, on 24, will move into second place with a win at Werder Bremen.
Dortmund, desperate to close in on Bayern ahead of Saturday's game, had to wait until two minutes from halftime to crack open a populous Fortuna defence.
Poland captain Blaszczykowski volleyed in after a lightning quick combination with Kevin Grosskreutz in the box.
Instead of finishing it off, however, Dortmund, looking tired after a busy month in three competitions, gradually allowed the visitors back into the game.
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.
Hamburg showed they can win this season even without injured Rafael van der Vaart, scoring three times in an exciting second half to beat Schalke 3-1 and move up to eighth and back into European contention.
A fierce 20-metre missile from Maximilian Beister in the 52nd put them ahead and Artjoms Rudnves tapped in a second goal from five metres in the 65th as Schalke scrambled in defence.
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.
- Sports & Recreation
- Stefan Reisinger
- Jakub Blaszczykowski