Gladbach cannot be faulted for effort as they went a fourth straight game without scoring, succumbing to yet another defeat in the battle of the Borussias.
54,000 souls watched on in the Borussia-Park as the Foals peppered the Dortmund goal, but Bürki repeatedly frustrated the hosts as he kept a valuable and remarkable clean sheet.
Watch: All 11 of Roman Bürki's saves vs. Gladbach!
With 11 saves, the Swiss custodian set a new shot-stopping record in the Bundesliga this season. No matter what Gladbach threw at him – and with 28 attempts on goal, they tried harder than in any other game this season – Bürki would not let them pass.
"We brought this home thanks to an extraordinary goal and an outstanding goalkeeper," said Peter Stöger, who became the first Dortmund coach to get through his first eight games in charge unbeaten.
Marco Reus' stunning strike would have won only a beauty contest had it not been for Bürki's bravery at the other end of the field, however, and the Swiss custodian had the bruises to prove it.
"I'm hurting all over," said Dortmund's hero Bürki. "That just goes to show how hard we worked for this win today. I try my best all the time and I am well aware that sometimes it doesn't always come off, but I'm really pleased that it did today.
"These are three very important points and now we can go to Bergamo for an important [UEFA Europa League] game with plenty of self-confidence."
Watch: Gladbach's Reece Oxford: "I don't know how we didn't score!"
Dortmund head to Italy on Thursday to defend a 3-2 advantage from the first leg at the Signal Iduna Park last week, safe in the knowledge they have a portable Yellow Wall to take with them.