- Mateo Retegui (56')
- Declan Rice (13')
- Harry Kane (44' Pen)
- Luke Shaw (80')
In a rematch of the final of the last European Championship, won on penalties by Italy, England were vastly superior in the first half and went into the break with a 2-0 lead courtesy of Declan Rice and Kane's record-breaking strike from the penalty spot.
But Italy fought back in the second half and halved their deficit in the 56th minute when Argentina-born Mateo Retegui scored on his Azzurri debut following a giveaway by Harry Maguire.
The complexion of the game shifted further with 10 minutes remaining when Luke Shaw was sent off for a second yellow card to leave England to defend the final minutes with 10 men.
Gareth Southgate's side, though, did enough to hold on and get their first away win against Italy since 1961.
Although there will be concern at how England lost their way in the second half, it proved the perfect response after the heartache of losing to France in the World Cup quarter-finals in December when Kane missed a crucial penalty.
This time he made no mistake after Giovanni Di Lorenzo was penalised for handball in the 42nd minute, finding the corner to claim another scoring record.
Kane was also involved in England's opener as his blocked shot fell for Rice to convert to silence the majority of fans inside the Stadio Diego Armando Maradona.
Italy, who beat England on penalties to win Euro 2020 at Wembley Stadium but failed to qualify for the World Cup, were far more dangerous in the second half after Argentina-born Retegui smashed a low shot past Jordan Pickford.
England sank deeper and deeper as they appeared to run out of legs but Italy struggled to create clear chances and suffered a first Euro qualifying defeat in 41 games.
It was England's first competitive victory over Italy since 1977 and meant Gareth Southgate has racked up 50 wins as the national coach since taking the job in 2016.
But the night belonged to Kane.
"I just want to say that this has been a really special night for me personally and a really special night for the team," Kane said. "It's the first time that England have won in Italy for a long, long time and to be part of that is amazing.
"I want to also say a big thank you to my teammates, to the staff, the fans, my family back home and my wife. It's a really special night and one that I'll never forget and I'm just so proud. And to everyone in here, thank you to everyone who has made this dream come alive."
Rooney, whose goals came in 120 games compared with the 81 it has taken Kane to move ahead of him, was quick to congratulate his former international team mate.
"I knew it wouldn't take long but that was quick. Great man, unbelievable goalscorer and an England legend. Congrats Harry!" Rooney said on Twitter.
It was the first time Naples had hosted the Azzurri for a decade but it all went flat for Roberto Mancini's team as they were outplayed in the first half.
Young midfielder Jude Bellingham ran the show in the early stages for England and he forced a superb save from Donnarumma when he let fly with a ferocious shot from distance.
From the resulting corner, the ball fell to Kane and when his shot was blocked by Leonardo Spinazzola it fell kindly for Rice to shoot past Donnarumma.
England looked dangerous every time they crossed the halfway line and Kane flashed a low ball across the face of the goal.
Kane's history-making moment was a touch harsh on Italy as referee Srdjan Jovanovic decided after checking a monitor that Di Lorenzo had used his arm as a cross came into the box.
Kane dispatched the penalty to put England in cruise control and Jack Grealish missed a glorious chance to make it 3-0 on the stroke of half-time.
Italy were a different proposition after the break and Retegui marked his debut with a clinical finish.
Mancini sent on Wilfrid Gnonto midway through the half and he caused all sorts of problems as Italy piled forward.
Shaw was booked for time wasting and a minute later received another yellow for a mistimed tackle and a flagging England had to dig deep to get over the line.
Information from Reuters was used in this report.
- Srdjan Jovanovic