The Bundesliga champions rang the changes for their final match of the league season, with the outgoing Thomas Muller leading Bayern's attack.
After a low-key start to the contest, Olise curled in an inch-perfect free-kick from 25 yards to give the visitors a 33rd-minute lead. Muller wasn't far away from getting on the scoresheet, but he couldn't keep his first-time shot under the bar.
Andrej Kramaric, who scored a hat-trick at home to Bayern last season and has eight goals against them in his career, should have equalised shortly after the break but his strike whistled past the post.
And in no time at all, they were punished as Olise's perfectly weighted pass was swept home by Joshua Kimmich, via a deflection, eight minutes after the interval.
Kane, who wasleft out of the starting lineup, rattled the woodwork shortly after coming on, but he showed the presence of mind to set up Serge Gnabry, who smashed home moments later in the 80th minute.
The England captain didn't have to wait long for his goal when he blasted the loose ball into the top corner against the fading hosts four minutes from time. Bayern managed to give Muller an ideal send-off, but the veteran will return for their Club World Cup campaign next month.