The England striker's double means he has now scored one more than the joint top scorers did in last season's entire Bundesliga campaign as his record-breaking start to life in Germany continues.
"I'm really enjoying it, the team around me are creating chances. I had a couple of chances in the second half, the two I scored were harder than the two I missed," Kane told Sky as Bayern set a German top-flight record of 42 goals after 11 matchdays.
"This is not a game people will remember at the end of the season but these are victories you have to get."
Kane turned superbly in the box on 14 minutes and fired in at the near post, and was somehow completely unmarked when he powerfully headed in a corner just before the break as Bayern - champions the last 11 seasons - went a point clear of Bayer Leverkusen at the top.
Heidenheim - in their first ever Bundesliga season - did respond with two goals in three second-half minutes before Bayern substitutes Raphael Guerreiro and Eric Maxim Choupo-Moting sealed the home victory.
Elesewhere, VfB Stuttgart beat Borussia Dortmund 2-1 thanks to a late penalty dispatched by the returning Serhou Guirassy as the hosts extended their advantage in third over the fourth-placed visitors.
Augsburg coach Jess Thorup - now unbeaten in his first four games - was again the comeback king in a 1-1 draw at home to Hoffenheim where a firecracker injured a home fan and led to a short match suspension.
Darmstadt drew 0-0 with Mainz, whose interim coach Jan Siewert picked up a fourth point in two games.
Bottom side Cologne drew 1-1 at Bochum in the late game.