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With Inter Milan losing, Arsenal are now the only team in the competition with a maximum 15 points and look all but assured of a place in the last 16.
Win ends Liverpool's losing streak; Chelsea-Ajax game sees first-half red card and three penalties.
PSG start Champions League defence in style.
Kingsley Coman opened the scoring in the sixth minute.
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.
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