Reus did manage to test Fahrmann on 67 minutes after Schalke survived a penalty appeal when Christian Pulisic went to ground, and the US worldwide fizzed a first-time shot over the bar four minutes later from the German's cross.
The last time these two rivals met, Dortmund, playing at the Westfalenstadion, blew a four goal lead, allowing Schalke to earn a point.
The result leaves BVB trailing second-placed Schalke by four points in the standings, but coupled with Bayer Leverkusen's victory over Eintracht Frankfurt on Saturday, the defeat means Dortmund are now fourth in the table on goal difference, with only a four-point cushion over RB Leipzig in fifth.
"We hope that it is not so bad", said coach Peter Stöger in the post-match press conference. "We'll have to look at the game again, I know there's not much use talking now about it like this".More news: Florida Woman Nabbed for Giving Child Pot and Meth
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Schalke looked more likely to score in the first half, though Dortmund's Marco Reus went closest when he drew a good save from Ralf Faehrmann with a free kick.
Konoplyanka broke the deadlock just five minutes after the restart as he latched onto Daniel Caligiuri's pass in behind the defence and slotted past Burki. Marco Pjaca sent the ball to Caligiuri, who stopped it for Naldo.
The local Ruhr Nachrichten newspaper reported the Belgian striker, who is on loan from Chelsea, is suspected to have suffered a lower-leg fracture.