The England captain put Bayern ahead from the spot after 15 minutes after Union's Benedict Hollerbach brought down Michael Olise on the edge of the box.

Kane turned provider just before half-time, tapping the ball into Kingsley Coman's path, the France forward blasting in over Union goalkeeper Frederik Ronnow.

Kane added another after 51 minutes, eagerly getting to a loose ball inches ahead of teammate Jamal Musiala to complete his brace.

Despite two consecutive Champions League losses at Aston Villa and Barcelona, Bayern have now scored 16 without conceding in their past four games against German opposition.

"We've not started the Champions League well, so the pressure is on in every Champions League game now," Kane said.

"I think if we use the confidence that we've played the last few games with, we can cause any team a lot of problems."

"There's still a long way to go, but we've got the right mentality and the right attitude," Kane told Sky.

"If we keep going like this, everything will be OK -- we're in good shape."

Having needed a win to avoid relegation on the final match day last season, Union now sit seventh and captain Christopher Trimmel told Sky "we can live with it -- Bayern were the favourites and have unbelievable quality."

Dortmund comeback

Borussia Dortmund beat RB Leipzig 2-1, handing them their first league defeat this season and relieving the pressure on under-fire coach Nuri Sahin.

Dortmund came into the game with four losses in their past five games, including Tuesday's German Cup elimination by Wolfsburg -- their earliest exit in 15 years.

Dortmund spurned several clear-cut chances early before Benjamin Sesko put Leipzig in front after 27 minutes, blasting in off the crossbar.

The hosts hit back three minutes later, Maximilian Beier tapping in a ball in the box for his first Dortmund goal since arriving in the summer.

With just over half an hour remaining, Beier looped a cross in to Serhou Guirassy, who headed Dortmund in front, his fifth goal in his past six league games.

The win sent Dortmund fifth while Leipzig now sit three points behind league leaders Bayern.

Kane's double took him past his main rival in this season's goalscoring battle, Omar Marmoush, who scored one and assisted two more in Eintracht Frankfurt's 7-2 demolition of hapless Bochum.

Hugo Ekitike scored a brace while Marmoush, Ansgar Knauff, Nathaniel Brown, Mahmoud Dahoud and Can Uzun all got on the scoresheet in the rout.

Marmoush now has 10 goals to Kane's 11 this season, but the Egyptian's six assists -- the best in the league -- are one more than the England captain's five.

Frankfurt leapfrogged champions Bayer Leverkusen into third place, six points behind leaders Bayern.

Bochum scored goals in each half through Dani de Wit and Philipp Hofmann but were thoroughly outclassed.

Bochum now have just one point from nine games to sit stranded at the bottom of the table after both promoted sides St Pauli and Holstein Kiel won on Saturday.

Kiel beat Heidenheim 1-0 at home thanks to a goal from Patrick Erras, for their first win in the top division, to go three points clear of Bochum.

Goals from Oladapo Afolayan and Andreas Albers took St Pauli to a 2-0 win at Hoffenheim, drawing them level with their opponents on eight points just above the direct relegation zone.

Elsewhere, Wolfsburg drew 1-1 at home with Augsburg.