Harry Kane equalled Robert Lewandowski’s half-season Bundesliga goalscoring record with a late strike but it was Jamal Musiala who provided the real cutting edge in Bayern Munich’s 3-0 victory over 10-man Hoffenheim.

The England striker clipped home left-footed from 12 yards in added time for his 22nd goal in 16 games to match the man whose number nine shirt he inherited following his summer move from Tottenham. Kane now has next week’s home match against Werder Bremen to surpass Lewandowski’s tally by the halfway stage of the campaign.

But on a night when the death of Bayern great Franz Beckenbauer was marked with a number of tributes – the outside of the stadium emblazoned with the words ‘Danke Franz’ – it was the mercurial talents of the 20-year-old Germany international Musiala which lit up the Allianz Arena and moved his side within a point of leaders Bayer Leverkusen.

The first of his two goals secured a new record for the German champions, who have now scored in 65 successive home league fixtures to beat their own Bundesliga record set between 1970 and 1974.

Musiala opened the scoring in the first half with a shot from a narrow angle which goalkeeper Oliver Baumann could have dealt with better before converting a simpler 70th-minute effort to secure the result on a night of half-chances and missed opportunities.

Grischa Promel’s 74th-minute dismissal for a second yellow card ended the visitors’ hopes of staging a late comeback, although that appeared unlikely after failing to capitalise on their only good spell of the game midway through the second half when Bayern goalkeeper Manuel Neuer marked his 500th club appearance with two good saves.

Bayern’s players all wore Beckenbauer’s number five during the warm-up, their match shirts also carried the words ‘Danke Franz’ and there was a period of silence before kick-off.

Once the game began, the hosts failed to create anything before they took the lead with their first shot in the 18th minute.

Hoffenheim were guilty of switching off as Bayern took a quick corner and that allowed Leroy Sane to picked out Musiala in space and he beat Baumann from the narrowest of angles via the far post.

It was Bayern’s 50th league goal in their 16th game and Hoffenheim’s 12th fixture without a clean sheet.

The only surprise was the home side’s failure to press home their dominance, the winter break appearing to have dulled their invention as all they could muster was a Raphael Guerreiro effort, teed up by Kane, which was comfortably turned around the post.

Hoffenheim’s best of limited opportunities saw Andrej Kramaric’s shot easily caught by Neuer.

Kane thought he had teed up Sane for Bayern’s second 10 minutes after half-time but it was ruled out for offside against the England captain, who continued to look one of Bayern’s biggest threats with a shot narrowly deflected wide.

Musiala then hit the post from distance with Thomas Muller unable to turn home the rebound and Konrad Laimer and Alphonso Davies were both denied by Baumann as Bayern began to ramp up the pressure.

But they were almost made to pay for not taking their chances as Neuer was forced into two great saves, first from Maximilian Beier’s close-range header and then Kramaric as he raced through on goal.

Even when Neuer was beaten by Beier’s volley, the ball crashed against the crossbar and that was to prove even more costly.

Musiala doubled his tally by converting Sane’s return pass and Kane grabbed his customary goal late on.