The Ruhr valley club, firm title contenders only a few weeks ago with six wins from their first seven league matches, have lost their winning touch and are without a Bundesliga victory since September, piling pressure on coach Peter Bosz.
Dortmund, who take on Tottenham Hotspur in the Champions League next week, are stuck on 20 points in third place with champions Bayern Munich, top on 26, taking on Augsburg on Saturday.
RB Leipzig, four points behind in second, travel to Bayer Leverkusen. Stuttgart, who have now won all of their 16 points this season at home, climbed to 11th.
A disastrous back pass from Marc Bartra allowed Chardac Akolo to slip in and put Stuttgart ahead in the fifth minute.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
Dortmund were in control and had their chances but with top striker Pierre-Emerick Aubameyang suspended, they lacked his finish.
"This defeat is very painful. We came here to win and we are very disappointed," Bosz told reporters. "It is ridiculous how we concede goals. But after the first goal but we played good football.
"Unfortunately, the second half was not that good but we will not give up. We will keep going."
Dortmund still managed a late first-half equaliser with Maximilian Philipp scoring on the rebound after Andre Schuerrle's penalty was saved.
But Josip Brekalo fired in through the legs of keeper Roman Buerki six minutes after the restart to restore their lead with a break that once again took the shaky Dortmund defence by complete surprise.
Eintracht had several more good chances to add to their tally with Brekalo and Berkay Ozcan as frustrated Dortmund ran out of gas.
(Reporting by Karolos Grohmann, editing by Ed Osmond)
