Follow Whatsapp Channel
The title win is the first major trophy for Kane, who two weeks ago broke a league record with his 60th goal in his first 60 league games for Bayern.
It was far from a comfortable evening for Inter, but they did just enough in a pulsating clash between the top teams from Serie A and the Bundesliga.
Frattesi tapped in from close range to stun the Bavarians, who had levelled three minutes earlier through substitute Thomas Müller.
Mueller has won numerous titles with the German club, including two trebles in the 2012-13 and 2019-20 seasons.
England and Germany have a fierce football rivalry which has played out at both the World Cup and Euros.
A 4-3 aggregate victory sealed Real's progress to a remarkable sixth Champions League final in 10 years and they will bid for a record-extending 15th title against Borussia Dortmund at Wembley on June 1.
Bayern, with only the Champions League title left to fight for, had scored twice in four minutes early in the second half through a Leroy Sane strike and Harry Kane penalty to turn the game around before Vinicius' spot kick.
City's Bernardo Silva and Mateo Kovacic both misfired in the shootout to put Madrid in the driving seat.
Xabi Alonso's team, who have now gone a league-record 29 matches without defeat this season to secure their first trophy since 1993, have a 16-point lead over Bayern with five matches remaining.
Paris St Germain's Kylian Mbappe scored twice to lead them into the Champions League quarterfinals.
Results 1-10 of 82
