All of the goals came in the second half on a remarkable afternoon in Munich, which also saw three red cards dished out in the first half of a match for the first time in Bundesliga history.
Kane scored his side's first, fifth and eighth goals during the rout, with his second strike coming from inside his own half as he lobbed the goalkeeper in sensational fashion.
The England captain's late hat-trick goal then took him up to 12 in his opening nine Bundesliga matches - more than any other player has ever managed in their first nine outings in the competition.
Kane also helped himself to an assist for Jamal Musiala's first of two goals, while Leroy Sane also helped himself to a brace and Thomas Muller came off the bench to add one more to his tally for the club.
Incredibly, the first seven of those goals came in the space of just 25 minutes as nine-man Darmstadt utterly capitulated against their 10-man hosts, before Kane fittingly had the final say to cap off the destruction.
All of the pre-match buzz had been centred around Manuel Neuer's return from a broken leg, ending a 350-day spell on the sidelines since his last appearance for the club.
However, the spotlight soon shifted away from the stalwart, and things even looked like they could end well for Darmstadt when Joshua Kimmich was shown a red card after only four minutes.
Numerical parity was restored within 20 minutes, though, as Klaus Gjasula was dismissed for Darmstadt, and Matej Maglica was also shown a straight red after 41 minutes to make it the first Bundesliga match in history to see three dismissals in the opening 45 minutes.
Sane saw a goal disallowed for offside before half time as the two sides went into the interval all square, but Bayern really made their man advantage count after the break as they put Darmstadt to the sword in ruthless fashion.
Kane, Sane and Musiala all struck within a nine-minute blitz to take the game away from the visitors in the blink of an eye, before Sane got his second of the game shortly afterwards.
In a match full of talking points and headline-worthy moments, it was Kane's second which will dominate the back pages as the summer signing reached new heights in his brilliant start to life in Bavaria, spotting the keeper off his line and launching a 55-yard effort over him and into the back of the net.
It was a moment that emulated similar goals from fellow English legends David Beckham and Wayne Rooney in the past, but Bayern did not stand on ceremony and, within two minutes, Muller added their sixth of the afternoon against a shell-shocked Darmstadt.
More to follow.