Robert Lewandowski carved his name in history with a double for Bayern Munich, while Schalke drew level with Dortmund.
Dortmund lost ground on Bayern Munich at the top of the Bundesliga on as they dropped points for the first time this season.
Borussia Dortmund returned to the top of the Bundesliga with a 3-0 victory over Bayer Leverkusen on Sunday.
Thomas Muller scored a 90th-minute penalty against Augsburg to keep Bayern Munich’s 100 per cent league record intact.
Thomas Muller struck twice as Bayern Munich beat Bayer Leverkusen 3-0 in the Bundesliga on Saturday, as Eintracht Frankfurt thrashed Stuttgart 4-1.
There were Bundesliga wins for Bayer Leverkussen and Bayern Munich, while Wolfsburg and Schalke were held to draws.
Chelsea have completed the signing of left-back Baba Rahman from Augsburg.
Bayern Munich will host Hamburg on the opening weekend when the 53rd Bundesliga season gets under way on August 14.
Augsburg booked their place in the Europa League next season by beating Borussia Monchengladbach 3-1.
Liverpool give U21s more game time than Premier League rivals but top flight lags behind Europe.
Hannover celebrated their first win of 2015 to move out of the bottom three with a 2-1 victory over Augsburg.
Augsburg kept their Europa League hopes alive with an unexpected 1-0 win at Bavarian rivals Bayern Munich.
Schalke ended a six-game winless run as Wolfsburg slipped to defeat, plus all the latest from the Bundesliga.
Augsburg only just managed to keep hold of their place inside the top six after a 0-0 draw at home to Cologne.
Borussia Dortmund closed in on the Bundesliga top six with victory, while Bayer Leverkusen stumbled to a 1-1 draw at Cologne.
Hamburg picked up their first win since early February by beating Augsburg 3-2.
Borussia Dortmund responded to the news of Jurgen Klopp's imminent departure with a 3-0 victory over Paderborn,
Augsburg moved five points clear of Hoffenheim thanks to a 2-1 win over Stuttgart.
Paderborn picked up a crucial three points in their battle to avoid relegation after beating Augsburg 2-1.
Schalke's hopes of a top-four finish receded further after a goalless draw at Augsburg on Sunday.