The Switzerland international, who has come in for criticism for displays in the Champions League in particular this season, endured another difficult 90 minutes as Dortmund slipped to a potentially damaging defeat that extends their recent run to one win in eight games in all competitions.
Much of the pre-match talk was dominated by the omission of Pierre-Emerick Aubameyang, dropped from the BVB squad for a breach of discipline, with Andre Schurrle handed his first league start of the season in the visitors' attack at Mercedes-Benz Arena.
Under-pressure head coach Peter Bosz had hoped for a strong reaction to the 3-1 loss to Bayern Munich before the international break but they were behind inside the first five minutes, as Chadrac Akolo capitalised on a dreadful mix-up between Burki and Marc Bartra.
Dortmund levelled just before the break, with Maximilian Philipp blasting home after Schurrle had a penalty saved, but Burki allowed Josip Brekalo's shot to slip through his legs six minutes into the second half after Dortmund's defence was caught cold by a counter-attack.
Andriy Yarmolenko had a second equaliser disallowed but Dortmund did not create much else to worry Ron-Robert Zieler in the Stuttgart goal, as they fell to a defeat that leaves them six points behind leaders Bayern, having played a game more.
It took only five minutes for Burki to be thrust back into the spotlight. Bartra allowed a stray long pass to bounce and passed the ball back to his goalkeeper just as Burki was running off his line, which resulted in the ball deflecting into the path of Akolo, who had a simple task of finishing into the empty net.
Dortmund sought a swift response, with Yarmolenko causing problems down the Stuttgart left and Schurrle looking a threat, while Mario Gotze forced a save from Zieler at the end of a promising team move.
Gotze was again denied by an athletic stop from Zieler after being teed up by Yarmolenko but, despite their dominance of possession, the visitors were becoming frustrated by a tough-tackling Stuttgart who were denying them clear-cut opportunities to equalise.
That was until first-half injury time, though. Gotze's cross was blocked by the elbow of Benjamin Pavard and, although Schurrle's penalty was saved by Zieler, Philipp reacted quickest to rifle the rebound high into the net.
However, six minutes into the second half, Dortmund's dreadful defending and Burki's low confidence was again exploited. Brekalo raced clear on the break with nobody but half-time substitute Dan-Axel Zagadou tracking him, before cutting back onto his left foot past the centre-back's poor challenge and firing a shot through the legs of Burki and into the net.
BVB heads had dropped again and only a superb sliding tackle from Bartra denied Takuma Asano from making it 3-1 from close range, while Berkay Ozcan nodded over the crossbar and Asano saw a header well held by Burki.
Yarmolenko lobbed Zieler in style but the goal was ruled out for a handball by the winger, and Dortmund got no closer to salvaging a point from another poor performance.
Pressure is now likely to mount on Bosz, with matches against Tottenham, Schalke, Bayer Leverkusen and Real Madrid to come in the coming weeks.
