Bayern were in control from start to finish in Bremen, with Leon Goretzka joining the England captain on the scoresheet in the 70th minute.
Kane has 26 goals in 22 Bundesliga games this season and 41 in all competitions, 13 of those from the penalty spot.
Bremen kept the league leaders at bay in the opening stages but Kane gave Bayern the lead with 22 minutes played, converting a penalty after VAR found Lennart Karl was felled in the box.
It was the third straight match Kane had given Bayern the lead from the penalty spot. Bayern doubled their lead three minutes later when Kane snuck a low shot in off the right post from the edge of the box.
Bayern captain Manuel Neuer was subbed off at half-time with a recurrence of a calf injury. Bayern put the game to bed when Goretzka swept home with 20 minutes remaining.