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.

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

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."

- Leverkusen beat Frankfurt -

Victor Boniface's 72nd-minute goal was the difference as Bayer Leverkusen beat Eintracht Frankfurt 2-1 at home.

Leverkusen were given an early chance when Amine Adli was felled in the box, sending Boniface to the spot after a long VAR review. The Nigerian's shot, too soft and central, was gobbled up by Frankfurt goalkeeper Kevin Trapp.

Just five minutes later, the referee was sent to the video screen again, this time finding a penalty for Frankfurt, with Robert Andrich lightly touching Omar Marmoush's foot.

Marmoush showed Boniface how it is done, blasting a low shot left to give the visitors the lead on 16 minutes. The Egyptian now has an incredible nine goals and five assists in just seven league games this season.

Andrich made good on his error soon afterwards, combining expertly with Adli and Martin Terrier to flit through the penalty area for a superb one-touch goal in the 25th minute.

Boniface would also redeem himself, giving Leverkusen the lead inside the final 20 minutes, heading in a deflected cross from substitute Florian Wirtz to put the hosts on course for victory.

Andrich told Sky Germany: "We were focussed and played good football.

"And there was a nice goal from me," he added with a grin.

The 30-year-old midfielder, who made his Germany debut last season after a career largely spent in the lower divisions, said of his performance: "I always have fun playing football, but I maybe have to work a bit harder than the rest."

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

Freiburg were three goals up at half-time, with Vincenzo Grifo, Philipp Lienhart and Christian Guenter scoring, before Augsburg's Phillip Tietz pulled one back in the second period.

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.