Bayern were comfortable against last season's unbeaten German champions, having already done the damage with a dominant 3-0 win at home in the first leg.
With the match scoreless at half-time, Leverkusen rolled the dice in search of the goals they needed but it was Bayern who struck, with Kane waltzing through to tap in a Joshua Kimmich cross.
With Leverkusen again pushing forward, the visitors added a second in the 71st minute, Alphonso Davies slamming a clever Kane chip low and hard to double Bayern's lead.
Kane, so often criticised for going missing in big games and scoring against the minnows, was again commanding, as he had been when scoring a brace in Munich.
The England captain showed finesse and physicality as he kept Bayern on track for a dream home final and a chance to exorcise the ghosts of their 2012 UCL final loss to Chelsea.