Dortmund rallied in the last 20 minutes, with chances falling to Christian Pulisic and Reus.
However, both teams staged a well-positioned defense and defused most opportunities in the opening period.
At the other end, Marco Reus forced a flying save from Ralf Faehrmann as his long range free-kick fizzed towards the top corner.
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. They remained nevertheless sloppy with their finish and failed to level the scores.
Schalke's Naldo applauds the fans at the end of the match.
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"We made individual mistakes", Dortmund coach Peter Stoeger said after his second defeat in 15 games.
"We played a great first half". "We'll have to look at the game again, I know there's not much use talking now about it like this". In the second half we scored the goals and defended well.
The Belgium worldwide has scored nine goals in 13 appearances, as Dortmund sit fourth in the Bundesliga table with four games of the season remaining.
The goal brought the game to life in the second half, and both Bremen's Moisander and Leipzig's Timo Werner missed golden opportunities to net a victor in the dying minutes.
Relegation-threatened Mainz host Freiburg to complete the 30th round of Bundesliga action on Monday.
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