Germany broke the deadlock when Jonas Hofmann fired the hosts ahead at the Allianz Arena, but Kane levelled from the spot with two minutes left.
Germany defender Nico Schlotterbeck stumbled into Kane in the area and the penalty was given after a VAR review.
The Tottenham striker moved into outright second on England’s list of all-time leading goalscorers, passing Bobby Charlton’s total of 49.
Gareth Southgate’s side remain bottom of Group A3 after losing 1-0 to Hungary in Budapest last Saturday.
Germany, who visit Hungary on Saturday, are a point above them in third as the Germans’ coach Hansi Flick extended his unbeaten run to 11 games, dating back to September.
Germany, playing in the shirts of their national women’s team, twice breached the England defence in the first half without reward.
Thomas Mueller lobbed the ball over England goalkeeper Jordan Pickford, but the whistle had already gone after an injury to Kalvin Phillips, who was replaced by Jude Bellingham.
Hofmann then broke clear and fired past Pickford, but after a VAR check, the effort was ruled offside.
Manuel Neuer, who captained Germany for the 54th time to overtake 2014 World Cup-winning skipper Philipp Lahm, made a reflex save to deny Bukayo Saka.
England struggled to get the ball into the box, especially in the first half, when Kane was closely marshalled by the German defence.
Germany were finally rewarded for their pressure early in the second period.
Joshua Kimmich split the defence with a pass into the feet of Hofmann, who drilled in a shot which Pickford could only get a glove to.
Only a fine stop by Pickford prevented Mueller marking his 114th international appearance with a goal.
Neuer again came to Germany’s rescue with another superb save to deny Kane from close range.
However, there was no denying England’s captain who sent Neuer the wrong way from the spot.