Leipzig's earlier 2-0 win at Mainz had allowed them to leapfrog Bayern into top spot, while Kane came into the match without a goal for club or country in four games -- his longest drought since moving to Germany.

Stuttgart, who surprisingly finished one spot ahead of Bayern in second place last season, held the hosts at bay but the dam eventually broke in the 57th minute, when Kane's long-range effort dribbled past goalkeeper Alexander Nuebel.

Kane added a second just three minutes later, clipping the ball through a crowded penalty box and past Nuebel to double Bayern's lead.

The England captain pounced on a loose ball on the 80-minute mark to bring up his third, chalking up his sixth hat-trick in Bayern colours and his 57th goal for the German giants in all competitions.

Kane had not scored in four games for club and country, his longest drought since moving to Germany.

The hat-trick was Kane's sixth for Bayern in the league as he brought up 57 goals in all competitions for the club.

"It was an important game for us coming off a few (bad) results. Here in front of our home fans, we took it up a level in the second half. It's what we want to do, we want to take teams to levels they can't," Kane told Sky Germany.

Coach Vincent Kompany said his side would "celebrate a little, but then get going again against Barcelona", who are managed by former Bayern coach Hansi Flick.

France forward Kingsley Coman scored in the final minute to complete the win.

Bayern were dealt a blow however, with midfielder Aleksandar Pavlovic picking up a shoulder injury.

Bayern sporting director Max Eberl said "it looks like he's broken his collarbone", while Kompany told reporters "it doesn't look good".

Earlier on Saturday, goals from Xavi Simons and captain Willi Orban took Leipzig past Mainz, just days out from their home Champions League clash with Liverpool.

Still unbeaten this season in Germany alongside Bayern, Leipzig took the lead after 20 minutes thanks to an excellent Simons solo goal.

Leipzig captain Orban tapped in a rebound from a Lois Openda cross to put his side 2-0 ahead.

Orban told Sky: "We could have finished things off earlier but we're happy with the win."

Elsewhere, Freiburg continued their impressive start to the season with a 3-1 home win over Augsburg to go into outright third.

Borussia Moenchengladbach striker Tim Kleindienst scored a double, days after making his Germany debut, in a 3-2 home win over former club Heidenheim.

Hoffenheim won their first game since their season opener, with Andrej Kramaric, Marius Buelter and Haris Tabakovic scoring in a 3-1 win over lowly Bochum, who sit last with just one point from seven games.

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