Kane has been directly involved in seven goals in his last 10 appearances against Manchester United
It was no secret that the Red Devils would have liked to have signed Kane from Tottenham in the summer, but instead England's captain and record goalscorer opted for a career in Germany that has begun in stellar fashion.
At the Allianz Arena on Wednesday, the 30-year-old claimed both an assist and scored from the penalty spot - after a VAR check to rule Christian Eriksen had handled in the box - to take his tally of goals this season to five in five games in all competitions.
It was a timely strike from Kane too as it came just after Rasmus Hojland had scored his first United goal to make it 2-1 early in the second half and give his side some hope of a result.
Before that, goalkeeper Andre Onana had undone a disciplined start from the visitors with a shocking error to allow Leroy Sane's drive to slip under him and find the net in the 28th minute.
Four minutes later, Serge Gnabry struck low and accurately inside the far corner to make it 2-0.
It is to the visitors' credit that they came out swinging to try and make a contest of it but their current fragility and lack of options from the bench as a result of numerous injuries undermined their ability to compete.
Casemiro showed dogged determination to smuggle a second in for United to give them a glimmer of hope but Mathys Tel snuffed that out by hammering a Bayern fourth high into the net in added time.
United were not finished, with Casemiro heading home Bruno Fernandes' free-kick from close range with almost the last kick of the game, but it was too late.
An opening-game loss at the six-time champions of Europe will not define the campaign, especially with FC Copenhagen and Galatasaray - who drew 2-2 earlier on Wednesday in Istanbul - both more beatable in the group, but they are now in dire need of a response to restore some focus and faith.
After a 2022-23 campaign of progress, United are again sailing in choppy waters.
Last season, Ten Hag looked to have steadied one of European football's biggest ships following the failure of the Ole Gunnar Solskjaer tenure and the ill-advised interim experiment with Ralf Rangnick.
Having led them to a first piece of major silverware in six seasons and back into the Champions League, optimism was high at the club ahead of this campaign.
But three defeats from the first five league games - their worst league start in a decade - has seen this rapidly evaporate and now they must digest a humbling start to their European campaign.
It could have been different. They could, and probably should, have led inside five minutes as Alphonso Davies' timely tackle stopped Facundo Pellistri tapping in but set up Christian Eriksen to fire an effort from close range straight at Sven Ulreich.
Similarly, at the start of the second half, had they been able to test Bayern's resolve for longer at 2-1 rather than conceding again inside five minutes they may have taken something.
And then at the end they showed fight to forge Casemiro's double only for that to be made moot by their soft concession of a fourth.
This is a United side undone by early-season results, injuries and costly moments of ineptitude.
Onana's error was a shocker and one a side with such fragile confidence can ill afford. It was followed by a period where players seemed happier to hide than rally in the face of adversity.
Before Wednesday's game, Ten Hag bemoaned that he had yet to field his strongest XI during his tenure and maybe it is only fair to judge him and his side this season when they are closer to that?
But this is still a United side with talent in it and one that needs to not only win at Burnley on Saturday but do so convincingly.
Bayern were not at their best. They have not been so for much of this season. They were also without suspended manager Thomas Tuchel as assistant Zsolt Low took charge on the touchline.
But they are a winning machine and with Kane in attack, supplemented by Sane, Gnabry and Musiala, they will be a test for any defence on the continent, let alone one as currently shaky as United's.
It was not Kane's best game, with him floating in and out of it, but he did what was required. His neat set-up enabled the opener and he made no mistake with a typically ruthless penalty.
They should have scored more, hitting the post twice after the break, and allowed United footholds in the game, but their ability to move rapidly up through the gears remains highly impressive.
That is 35 games unbeaten now for the German champions in the group stage of this competition and 15 straight home wins. It gives them early control of Group A.
-- Courtesy of BBC Sport