Kane’s two goals came from first-half penalties, while Diaz added the next three goals to see Bayern advance to 54 points from 21 games, well clear of second-placed Borussia Dortmund who won 2-1 at VfL Wolfsburg on Saturday.
Hoffenheim had Kevin Akpoguma sent off for a 17th-minute foul that allowed Kane to open the scoring from the spot but they equalised through Andrej Kramaric before Bayern took control and imposed themselves on the under-strength visitors.
Hoffenheim stay in third spot on 42 points as their run of five successive Bundesliga wins came to an end.
Akpoguma was sent off for tugging down Diaz as the Colombian winger burst into the Hoffenheim area and Kane tucked away the resultant kick in the 20th minute.
Despite the numerical disadvantage, Hoffenheim responded with an attacking approach and, after spurning good chances,pulled level when Bayern’s veteran goalkeeper Manuel Neuer blundered with a casual clearance that was picked off by Fisnik Asllani, who then teed up Kramaric to make it 1-1.
Another foul on Diaz, this time by Vladimir Coufal, handed Bayern a second penalty on the stroke of halftime and Kane netted again for his 24th goal of the Bundesliga season.
Coufal was cautioned but, unlike Akpoguma,was not sent off.
England captain Kane then led a swift counter-attack two minutes into stoppage time at the end of the half, before setting up Diaz for a 3-1 lead at the break.
Neuer made a point-blank stop from Asllani in the 58th minute to atone for his earlier error before Diaz got his second goal four minutes later, with Michael Olise squaring for an easy-looking finish.
Diaz completed hishat-trick in the last minute, collecting the ball on the right of the Hoffenheim area and then running inside before picking his spot and hitting the ball wide of goalkeeper Oliver Baumann into the corner of the net.
Bayern have now scored 79 goals in this Bundesliga campaign, prompting coach Vincent Kompany to praise his strikeforce.
“They simply never stop. If things get a little less exciting, they’re right back at it. They’re always hungry to attack,” he said.