Haller scored in the 58th minute, and with six minutes to go he scored his second goal of the day and won, lifting Bayern into first place.
Julian Brandt capped off the victory with a goal in the compensatory time.
The club from the Ruhr Valley, which last won the title in 2012 under then-coach Jurgen Klopp, scored 70 points, two points ahead of Bayern.
The Bavarians suffered a shock 3-1 loss to RB Leipzig on Saturday.
In a one-sided first half, Dortmund took 16 shots on goal against one for Augsburg and also hit the post thanks to a goal from Niklas Süle, but could not score even when the hosts were left ten men down after Felix Uduohai’s suspension in the 38th minute.
Emre Kahn also hit the woodwork after the resumption of play, but Augsburg ended up scoring Haller with a shot off the post.
Augsburg immediately responded with a chance of their own, but Dortmund keeper Gregor Kobel successfully stopped Irwin Cardona’s shot from 10 meters.
Haller, who had missed most of the season after being diagnosed with testicular cancer last year, calmed Dortmund’s nerves with a goal, and Brandt completed the win in regulation time.
In the last match, Dortmund takes on Mainz 05, and Bayern, who have won the last 10 league titles, travel to Cologne in the season finale.
Three-time champion City, who sealed the title when Arsenal beat Nottingham Forest on Saturday, have won 12 straight matches in the top division.
They have 88 points from 36 games, seven more than Arsenal, who have played 37 games. Frank Lampard’s Chelsea are 12th with 43 points and one game to spare.
Alvarez scored in the 12th minute for virtually second-team City, sliding the ball under goalkeeper Kepa Arrizabalaga off a pass from Kyle Walker. Another goal was cancelled due to a handball early in the game.
With nothing on the line on Sunday, and with two great matches looming on the horizon, the FA Cup and Champions League finals, Pep Guardiola left most of the game on the bench, including goal scoring machine Erling Haaland. City still dominated, proving that they are a well-oiled machine, no matter what parts the manager has to work with.
City became champions for the third consecutive season and fifth in six years a day earlier than expected, when a 1-0 loss to Arsenal dashed all Londoners’ hopesto name them.
The mood on Sunday was festive. Chelsea sportingly gave a guard of honor to the City players who watched the Arsenal game together the night before, and after the final whistle thousands of fans poured onto the pitch.
Haaland was replaced late and did not extend his record of 36 goals in a single Premier League season.