The England striker netted twice to cancel out Andriy Yarmolenko's 11th-minute equaliser after Son Heung-min gave Spurs the lead to give the North Londoners the ideal start to this season's Champions League adventure.
In addition, Wednesday night's win over the Bundesliga giants is only the second in 12 outings at Wembley Stadium for Spurs, and Kane has urged his side to make the most of their games at their temporary home.
Kane told BT Sport: "It's a massive win, nights like this at Wembley, we have to take advantage of it. Last season our downfall was the games at home. It was a more experienced performance from us tonight.
"In the Champions League you have to be smart. You can't always press teams on a big pitch, we took advantage on the counter-attack and exploited the space they left in behind."