Kane opened the scoring after 11 minutes following a spectacular save from Mouez Hassen after John Stones' effort.
Already, Gareth Southgate's side have more wins than they managed in Brazil in 2014, and with Kane on fire in attack, there could be more to come.
Out in Volgograd, where the game took place, 2,000 or so hardy supporters erupted into ecstasy. We had a lot of bug spray on and that was important.
"Maybe tonight we could have run out of time".
Danny Welbeck has the best goal tally of any player in Southgate's squad, with 16 goals in 29 appearances, but the injury-jinxed Arsenal forward has only scored twice in five appearances under the current manager and his involvement in Russian Federation is likely to be as an impact substitute when, or if, England are chasing the game.
That was exactly what England did, but they needed Kane to be at his predatory best.
Carlos Queiroz hails Iran's opening World Cup win over Morocco as 'beautiful'
The lesson here? In the World Cup , you simply can not afford to lose focus until the final whistle blows. The state in Iran has banned women in the country from attending male-only sports events since 1979.
2,000 families separated at USA border in six weeks
Franklin Graham, son of late reverend Billy Graham and a staunch Trump supporter, said the separation policy was "disgraceful". This is the Trump administration's decision and they could put an end to this immoral policy today.
Brazil held by plucky Switzerland
Zuber thumped home a header from Xherdan Shaqiri's corner with the Brazilians calling for a free-kick for a push on Miranda. The match was pretty much all Brazil from the beginning, but outside of its lone goal, the ball just didn't want to go in.
It is England's second group stage game as they look to follow up their opening victory over Tunisia with all three points against minnows Panama.
If England march into the quarter-finals with a dominant win in the last-16 and show signs that their frailties of yesteryear have been erased, then the hype machine can crank into gear with justifiable glee.
"I did not feel the midges because I was so focused on the team, on the game", Tunisia's Nabil Maaloul said.
Backing Linker, on wrote: "Disagree was not a lucky win, are you sure you watched the game?"
Jesse Lingard and Dele Alli were also below-par in Volgograd - Lingard missed three clear chances to add to his one goal in 13 appearances - but Sterling is the one whose performance level drops furthest when he changes his club shirt for an England jersey.