Sven Bender put the home side ahead before netting in his own goal and Nuri Sahin's strike was canceled out by a Ji Dong-Won, who Dortmund has a pre-contract deal with.
The South Korea international joined Augsburg on a short-term deal from Sunderland earlier this month, before then being announced as a close-season signing for BVB just 24 hours later.
The script was written for Ji to grab the headlines at Signal Iduna Park on Saturday and he did not disappoint - glancing a 72nd-minute header past Roman Weidenfeller shortly after coming off the bench to steal a share of the spoils for Markus Weinzierl's side.
The Schwarzgelben went ahead after just five minutes courtesy of Sven Bender, who stole in at the back post to nod home Marco Reus' in-swinging free kick.
However, the Germany international went from hero to villain for the home side as he turned Andre Hahn’s cross past his own keeper 10 minutes after halftime.
Nuri Sahin looked to have spared his midfield partner's blushes with a delightful 20-yard free kick 11 minutes later, but Ji had other ideas, as he headed another dangerous delivery from Hahn past the helpless Weidenfeller.
Dortmund dominated the vast majority of the game, but uncharacteristically profligate finishing from the likes of Robert Lewandowski and Reus ensured Jurgen Klopp's wait for a first league win since November goes on.
Klopp's day got off to a bad start as Jakub Blaszczykowski suffered a suspected sprain early on, but Dortmund went ahead soon after courtesy of some quick thinking from Reus and Bender.
Reus picked himself up after being fouled on the left to curl an inviting delivery to the back post, where Bender got in front of Matthias Ostrzolek and nodded his first goal of the season past Marwin Hitz.
Dortmund settled after taking the lead, and could have extended the advantage on 25 minutes through Lewandowski.
The Bayern Munich-bound striker raced clear but lacked composure when one-on-one with the goalkeeper, as Hitz smothered his tame effort.
Reus was then guilty of spurning Dortmund’s best chance to give the team some breathing space when he collected a slack Augsburg pass but sliced his shot wide from 18 yards with only Hitz to beat.
Dortmund picked up where it had left off after the interval, but Augsburg fortuitously drew level against the run of play on 55 minutes thanks to Bender.
Slick interplay between Paul Verhaegh and Hahn resulted in the latter firing in a dangerous low cross that the 24-year-old Dortmund man diverted past Weidenfeller at the near post.
Sahin appeared to have rescued all three points when he restored the home side’s lead with a superb free kick that bent into the top corner 11 minutes later, but Ji had the final say to extend Augsburg's unbeaten Bundesliga run to six games.