The England captain netted a penalty in the 44th minute of the Group C encounter in Naples after a Giovanni Di Lorenzo handball.
Tottenham striker Kane had been locked with Wayne Rooney on 53 goals for his national team after missing a penalty in England’s World Cup quarter-final defeat by France in December.
The 29-year-old has reached the record total in 81 matches, during which time he has become a fixed presence in attack for a team which has performed well at recent major tournaments.
He was made captain by manager Gareth Southgate for the 2018 World Cup in Russia, where he won the Golden Boot as England reached the semi-finals for the first time since 1990.
He also scored four times at Euro 2020, including the winner in the semi-final against Denmark before his team fell at the final hurdle against the Italians.
Last month he broke Tottenham’s all-time scoring record with his 267th goal for his boyhood club, surpassing the total set by club icon Jimmy Greaves in the 1960s.