High-flying Hoffenheim came into the match full of confidence off the back of five straight wins in the Bundesliga.
The side is defying all pre-season expectations to occupy third place in the standings and got off to a fast start against the defending champions.
However, disaster struck in the 17th minute when Kevin Akpoguma fouled Luis Diaz in the penalty area to deny a goalscoring opportunity.
The action resulted in a penalty for Bayern and a red card for Akpoguma, meaning they would need to play for over an hour with just 10 men against the league's best side.
Harry Kane stepped up to convert from the penalty spot to give the home side the lead.
The visitors did well to create pressure despite being a man down, with Ozan Kabak heading a chance against the crossbar and Andrej Kramaric being denied by a sharp Manuel Neuer save.
They kept at it, though, and managed to draw level in the 35th minute after a chipped pass from an out-of-position Neuer was intercepted by Kisnik, who played the ball on to Kramaric for an easy finish into an empty net.
Unfortunately, the effort expended to keep themselves in the game with a man down was too much to maintain for Hoffenheim and things began to fall apart towards the end of the first half.
Kane scored another penalty in the 45th minute before the English striker spearheaded a brisk counter-attack by playing in Diaz to score two minutes into stoppage time to ensure Bayern would take a 3-1 lead into the break.
The Bavarians dominated the second half against a spent Hoffenheim, with Diaz adding his second of the game after getting on the end of a lovely Michael Olise cross.
He completed a fine hat-trick in the 89th minute with a deft curling strike into the bottom corner to complete the scoring and secure a 5-1 win for the home side.
Elsewhere in the Bundesliga on Sunday, RB Leipzig moved back into the top four with a 2-1 victory over FC Koln at RheinEnergieStadion.
Christoph Baumgartner opened the scoring for the visitors in the 29th minute with a powerful header after getting on the end of a David Raum free kick.
The home side fought back well and found an equaliser through Jan Thielmann in the 51st minute, but Baumgartner and Leipzig responded just five minutes later to restore their lead and secure the victory.