Sebastien Haller emerged as the hero, netting two crucial second-half goals to secure the win and propel Dortmund two points clear of rivals Bayern Munich, who suffered a 3-1 defeat to RB Leipzig the previous day.
Dortmund now faces a pivotal final match against Mainz, needing to outperform Bayern's result to claim the coveted Bundesliga shield for the first time since the 2011-2012 season.
The game remained goalless until the 58th minute when Haller capitalized on a rebound, slotting home the opening goal.
The French striker, who triumphantly returned to the pitch after battling testicular cancer, brought sheer joy to the travelling fans by adding another goal with only six minutes remaining. Julian Brandt sealed the emphatic victory with a goal in injury time, sparking scenes of celebration.
Dortmund, aware that a win would grant them control of the title race, displayed dominance in the first half but struggled to find the breakthrough. Haller came close earlier, forcing a fingertip save from Augsburg goalkeeper Tomas Koubek. Julian Brandt also had an opportunity but was denied by Koubek when one on one.
Late in the first half, Augsburg's Felix Uduokhai received a red card for a foul on Donyell Malen, reducing his team to 10 men. Despite their numerical disadvantage, Augsburg fought valiantly to salvage a point.
Haller's breakthrough arrived in the 58th minute as he latched onto a rebound off Koubek, expertly guiding the ball into the far corner. With just over five minutes remaining, Haller struck again, capitalizing on a Marco Reus shot that rebounded off the post, effectively securing Dortmund's 2-0 lead and igniting chants of "German champions, only Dortmund" from the visiting fans.
In the closing moments of the match, Dortmund captain Mats Hummels suffered an unfortunate injury, leaving the field with assistance after a blow to the face. Nico Schlotterbeck, Hummels' replacement, orchestrated the final goal, providing the assist for Brandt to seal the 3-0 victory.