South Korean Ji Dong-won beat keeper Roman Weidenfeller at the second attempt in the 33rd minute to put the visitors ahead.
Dortmund, who had hit the post through Mario Goetze in the ninth minute, dominated late in the first half but could not make their pressure count until Ousmane Dembele levelled two minutes after the restart.
The hosts had numerous chances in a one-sided second half with Pierre-Emerick Aubameyang, the Bundesliga's top scorer, going close half a dozen times.
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Dortmund are fourth on 27 points, nine points adrift of leaders Bayern Munich and RB Leipzig, who face each other on Wednesday.
"I think the game tonight reflects our first half of the season," said Dortmund coach Thomas Tuchel after Dortmund's third consecutive league draw.
"We are being punished too often. We should be able at some point to keep a clean sheet and win 1-0," Tuchel said. "We will obviously not stop working at it. We need to be consistent in our competitions."
Eintracht Frankfurt moved up to third on 29 after beating 10-man Mainz 05 3-0 with Branimir Hrgota scoring twice as they secured a fourth victory in their last seven league games.
Mario Gomez's winner gave VfL Wolfsburg a 2-1 victory over Borussia Moenchengladbach that left both teams on 16 points and heaped further pressure on Gladbach coach Andre Schubert following their fifth loss in the last seven games.
Hamburg SV climbed into the relegation playoff spot after edging past Schalke 04 2-1.
(Reporting by Karolos Grohmann; Editing by Toby Davis)
