- Felix Uduokhai (38')
- Sébastien Haller (58', 84')
- Julian Brandt (90'+3')
Haller broke the deadlock in the 58th minute and tapped in his second goal of the afternoon six minutes before the end to seal the win that lifted them above Bayern Munich and into top spot.
Julian Brandt completed the win with a stoppage-time goal.
The Ruhr valley club, whose last title win came in 2012 under then coach Jurgen Klopp, are two ahead of Bayern on 70 points.
"We have suffered and we had to sweat a lot, not only this season," said Dortmund coach Edin Terzic. "Now it is about taking that last step together with our fans in our stadium in our city and bring the league trophy finally back to Dortmund.
"This has not been the season of missed chances, but the season of setbacks. It is now about taking that last step."
In a one-sided first half Dortmund had 16 shots on goal to Augsburg's one and also hit the post through Niklas Sule, but could not score even when the hosts were left with 10 men following the dismissal of Felix Uduokhai in the 38th.
Emre Can also hit the woodwork after the restart, but they finally broke the deadlock through Haller when he slotted in off the post.
Haller, who had missed much of the season after being diagnosed with testicular cancer last year, settled Dortmund's nerves with a tap-in before Brandt completed their win.
Dortmund host Mainz on the last matchday while Bayern, who have won the last 10 league titles, travel to Cologne in their season finale.
"If some told me six months ago that I would be in this situation today I would not have believed them," Haller, who underwent surgery and chemotherapy before his return to action in 2023, said.
"We have invested a lot and now we have a chance to achieve something big. There is no magic. It is about investing. Then it comes."
- Tobias Welz
|1. FC Heidenheim 1846||14||4||2||8||-9||14|
|1. FC Union Berlin||13||3||1||9||-13||10|
|SV Darmstadt 98||14||2||3||9||-20||9|