The hosts dominated proceedings from the beginning and broke the deadlock after around 30 minutes into the game.
Leroy Sane’s powerful shot hit the post and went in off Felix Uduokhai to put them 1-0 ahead.
The Bavarians were soon awarded a penalty for Niklas Dorsch’s handball and Kane made no mistake from the spot to extend their advantage just before the interval.
The England ace completed a double in the 69th minute, lofting a calm finish after Alphonso Davies found him with a good pass.
Augsburg pulled one back through substitute Dion Beljo but that only served as a late consolation for the visitors.
Thomas Tuchel’s side will now take the trip to North Rhine-Westphalia to take on Borussia Monchengladbach, available to watch via Bundesliga live streams.
Kane has taken the German league by storm since making the €100 million move from Tottenham Hotspur.
He scored on his debut against Werder Bremen, helping his side to an emphatic 4-0 victory.
And then on Sunday, the experienced striker netted a brace against Augsburg to make an excellent start to life in Germany.
Kane looked to be staying at Tottenham after the Premier League outfit rejected several offers from Bayern.
However, they continued their pursuit and ultimately managed to wrap up a deal for the 30-year-old.
It is still too early to offer an opinion but all the signs suggest he will be a great hit at the Allianz Arena.
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