Borussia Dortmund need just one more win in next weekend's season finale to end Bayern Munich's 10-year reign as Bundesliga champions following a 3-0 victory at Augsburg.
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Sebastien Haller, who missed the first half of the season due to cancer treatment, grabbed the first two goals on 58 and 84 minutes on Sunday.
The forward expertly found the far corner after a mistake by Maximilian Bauer for the opener and then slotted in an easy second.
"Now we have to sleep six times, and be awake once," said Dortmund coach Edin Terzic, whose team host Mainz for their final game on Saturday while Bayern visit Cologne.
"Now we have a huge chance to achieve something big.
"We knew we have wasted a few opportunities in the past. I'm happy and proud of the team. It is something beautiful."
Julian Brandt added a jubilant third in stoppage time.
Dortmund, last champions in 2012, moved two points above Bayern at the top after taking full advantage of Thomas Tuchel's side being stunned 3-1 at home on Saturday by third-placed RB Leipzig.
The campaign concludes next Saturday when Dortmund - formerly coached by Tuchel - host Mainz and Bayern are at mid-table Cologne.
Jude Bellingham was out injured for the patient visitors, who had missed a raft chances at 0-0, with Niklas Sule and Emre Can both hitting the post.
But Dortmund were helped by Felix Uduokhai being dismissed on 38 minutes for a debatable professional foul.
It is the most thrilling title duel in Germany for over a decade, but the relegation battle will also be decided when the season climaxes.
Augsburg, in 14th, are not yet safe from the drop.
VfB Stuttgart moved out of the relegation places after a battling 4-1 win at Mainz, dropping Schalke back into the automatic drop zone with the one round of matches left.
Stuttgart rose up to fourth-bottom, a much better goal difference lifting them above Bochum, who occupy the relegation play-off spot.
Schalke are a point adrift of both while bottom side Hertha Berlin have already gone down.
Ninth-placed Mainz, now with no chance of a European berth next season when they face Dortmund, took the lead when Marcus Ingvartsen poked in following a corner amid static Stuttgart defending.
But Japan's Wataru Endo levelled for Stuttgart before the break with a superb shot with the outside of his boot.
Endo had kept Stuttgart in the Bundesliga on the final day last season with a stoppage-time goal and helped his side at a crucial time again in Mainz, with Serhou Guirassy then rising highest to head in a corner on 64 minutes to complete the turnaround.
Chris Fuhrich made it 3-1 soon after and Tanguy Coulibaly netted on the break in injury time for only a second away victory this term.
Stuttgart must win Saturday's showdown at home to Hoffenheim if the 2007 champions are to definitely save themselves once more.
A tired-looking Bayer Leverkusen squandered a two-goal lead to draw with Borussia Monchengladbach 2-2.
It's Leverkusen's sixth game in a row without a win, including two Europa League semi-final games against Roma.
Their 14-game unbeaten run was ended by Cologne in the Rhine derby on May 5 and Xabi Alonso's team haven't recovered.
Australian Associated Press
