Bayern returned to action after a costly international break which saw Vincent Kompany lose Alphonso Davies and Dayot Upamecano to injuries. However, Bayern needed just 17 minutes to open the scoring when Kane ended a mini-drought in the Bundesliga with the opening goal. Jamal Musiala won possession deep in the St Pauli half and, although he was then tackled, the ball fell kindly to the overlapping Michael Olise to cross for Kane to convert from close range.
Yet St Pauli stunned the hosts by grabbing a deserved equaliser just 10 minutes later A good move down the right saw the ball curled into the penalty area and knocked past goalkeeper Jonas Urbig by Elias Saad after a great run forwards into the box.
Bayern hit back early in the second half through Leroy Sane. Again Olise was the creator, the France international clipping a ball over the top for Sane to chest down and smash a low shot home to make it 2-1 to the hosts. Olise then could have had a goal of his own but crashed a powerful shot into the side-netting after good work from Musiala.
Kompany's side went on secure the points by adding a third with just 20 minutes remaining. Kane played a one-two with Olise and then scampered forwards before sending the ball in for Sane to score his second of the match.
St Pauli did reduce the deficit deep into stoppage time through Lars Ritzka but it proved to be only a consolation as Bayern restored their six-point lead at the top of the Bundesliga.