The thumping win over mid-table Wolfsburg leaves second-placed Dortmund six points behind Bayern, who are away to Arminia Bielefeld on Sunday.
Bundesliga: Dortmund held to 1-1 draw at Augsburg; Leipzig earn 1-0 win at Bochum to remain fourth on table
Thorgan Hazard's first-half goal gave Dortmund the lead in Bavaria, until Augsburg's pressure paid off and substitute Bazee headed in off the crossbar in the 78th minute.
Jude Bellingham and Mahmoud Dahoud scored late goals as Borussia Dortmund came from behind to seal a dramatic 3-2 win at Eintracht Frankfurt.
The Bundesliga leaders suffered only their second league defeat this season and their third in all competitions while Augsburg escaped the bottom three.
The result lifts Leipzig to seventh, six points behind leaders Bayern Munich, who host Eintracht Frankfurt on Sunday.
Bundesliga: Robert Lewandowski grabs hattrick as Bayern rout Hertha Berlin; Leverkusen beat Augsburg
Cologne enjoyed a 2-1 win over promoted Bochum, Mainz beat promoted Greuther Fuerth 3-0 and Eintracht Frankfurt were held 1-1 at Arminia Bielefeld.
Bundesliga: Erling Haaland nets twice, assists thrice as Dortmund rout Frankfurt; Stuttgart beat Greuther Fuerth
Defending champions Bayern Munich, who are bidding for a tenth straight league title, kicked off the new season with a 1-1 draw at Moenchengladbach on Friday.
Bundesliga: Bayern striker Robert Lewandowski breaks 49-year-old scoring record with 41st goal of season
Lewandowski scored in the 90th minute of Bayern's 5-2 home win over Augsburg having equalled Mueller's record of 40, which was set in 1971/72, last weekend.
Bayern's players, substitutes and team staff formed a guard of honour for Lewandowski to run through after he tied Müller's 49-year-old record with a penalty in the 26th minute in Freiburg.
A four-match winless run has seen Augsburg slip to just four points above the relegation play-off spot with three games remaining in the season.
Bundesliga: Robert Lewandowski's hattrick helps Bayern Munich beat Borussia Dortmund; Hertha Berlin edge Augsburg
Lewandowski completed his hattrick in the last minute, just after Leon Goretzka put Bayern ahead for the first time. Erling Haaland had fired the visitors into an early two-goal lead.
Bundesliga: RB Leipzig inch closer to Bayern Munich at top with win over Hertha Berlin; Bayer Leverkusen beat Augsburg
A superb second-half strike by defender Nordi Mukiele and a header from centre-back Willi Orban sealed the victory.
Bundesliga: RB Leipzig warm up for Champions League clash against Liverpool with 2-1 win over Augsburg
In sub-zero temperatures, Leipzig warmed up for Liverpool with goals by Dani Olmo and Christopher Nkunku giving them a 2-0 lead at half-time.
Bundesliga: Robert Lewandowski’s penalty helps Bayern Munich consolidate lead; Arminia Bielefeld beat Stuttgart
Bayern Munich stayed four points clear of Leipzig, who earned a hard-fought 1-0 victory over Union Berlin thanks to Emil Forsberg’s 70th-minute strike.
Bundesliga: Florian Grillitsch's brace helps Hoffenheim ease past Augsburg to end seven-match winless run
Grillitsch gave Hoffenheim the lead in the 17th minute with a header at the far post off a cross from his fellow Austrian Christoph Baumgartner to cap an incisive team move.
Lewandowski, who played for Dortmund between 2010 and 2014, took his tally to 17 goals in 13 games against his former club. He also clocked up his 11th goal in just six Bundesliga appearances for Bayern so far this season.
Bundesliga: Borussia Dortmund dig deep to edge past Hoffenheim; Bayern Munich defeat Arminia Bielefeld
Borussia Dortmund needed substitutes to dig them out of a hole for a 1-0 win against Hoffenheim, while Bayern Munich had no such difficulties as they romped to another Bundesliga rout on Saturday.
Bundesliga: Robert Lewandowski nets four goals as Bayern Munich clinch seven-goal thriller against Hertha Berlin
The victory got Bayern back to winning ways after their record 23-match winning streak was ended by a 4-1 defeat at Hoffenheim last Sunday.
Dortmund had three times as many shots on goal and dominated with 80 percent possession, which left their Swiss coach Lucian Favre to admit, "we are very disappointed, it's hard to accept this defeat".
Lichtsteiner said in a Swiss football federation statement it became clear after Euro 2020 was postponed by one year because of the pandemic that it was “a good moment” to retire.