"We've got some quick guys up front and with them we really hurt Dortmund."
Stung by a midweek German Cup elimination by third-division Saarbruecken, Leverkusen's 3-2 win at Hoffenheim on Saturday meant injury-hit Bayern were five points behind Xabi Alonso's side at kickoff.
The visitors however crafted the perfect response, scoring two goals in the opening nine minutes to grab a hold on the match.
The former Man City winger laid on Bayern's second on the counter, slipping a perfect pass across the face of goal for Kane to tap in.
Unbeaten at home for more than a year, Dortmund were shellshocked by the power of the supposedly weakened visiting side.
Dortmund manager Edin Terzic made four changes early in the second-half as his side hoped to chase the game but Bayern scored next, Kane stroking in a controlled finish with 15 minutes remaining.
"The way we played during the week, it was bitter" Neuer said of the German Cup loss "but we showed what we can do today."
"Bayern were simply more aggressive in the duels and simply more dangerous on the counter attack" said Dortmund 'keeper Gregor Kobel, who made several key saves early in the second half.
The England captain scored again in injury time and now has 15 league goals in 10 matches since joining Bayern from Tottenham in the summer.
- Leverkusen on top -
Earlier on Saturday, goals in each half from Alex Grimaldo took Bayer Leverkusen to a 3-2 win at Hoffenheim.
Unbeaten Leverkusen, who have now won nine and drawn one in the league, made difficult work of the win, allowing Hoffenheim to score twice in two minutes to let a 2-0 lead slip.
The visitors re-took the lead thanks to a late Grimaldo goal.
"I gave Grimaldo a kiss," said Leverkusen goalkeeper Lukas Hradecky, whose howler let Hoffenheim back in the game.
"Last year we would not have won this game."
With Leverkusen cruising, goalkeeper Hradecky hit a low pass while roaming well outside his box and Anton Stach took advantage of the error by driving a long-range shot home.
Former Manchester United striker Wout Weghorst unleashed a stunner just two minutes later to bring the home side level but Grimaldo curled in the winner with 20 minutes remaining, his fifth league goal of the season since arriving from Benfica in the summer.
"That was a fight" Wirtz told Sky. "We did it hard... but wins like that are also nice."
Union Berlin's woes continued ahead of Wednesday's Champions League visit to Napoli, losing 3-0 at home to Eintracht Frankfurt thanks to a first-half double from Omar Marmoush and a late strike from Nacho Ferri.
The loss, Union's 12th in a row in all competitions, means the side has now tasted defeat eight times so far this season -- equal to their final total at the end of the last campaign.
"It's difficult to talk about being in a relegation battle," said captain Christopher Trimmel, "but we simply need to do it."
Elsewhere, Mainz won their first match of the season, shocking RB Leipzig 2-0 at home thanks to goals from Lee Jae-sung and Leandro Barriero, just days after sacking manager Bo Svensson.
Cologne were held 1-1 at home to Augsburg, meaning Steffen Baumgart's side will finish the match in last place.