Kane completed his hat-trick shortly after the hour mark to go top of the tournament's goal chart and make Felipe Baloy's late consolation nothing to worry about as the Three Lions eased into the last 16.
Having scored an injury-time victor to beat Tunisia 2-1 in their opening group game, England smashed minnows Panama 6-1 on Sunday.
They conceded two penalties in the first half and Kane was on hand to gleefully dispatch them.
England's Harry Kane was the leading goal scorer in their match against Panama.
England led 5-0 at halftime, with Kane's two first-half goals coming from penalties.
Nobody would have thought that after just two games, England would have scored eight goals.
Harry Kane now has a permanent souvenir from the World Cup.More news: Apple releases iOS 12 Public Beta
The third goal of the game, scored by Jesse Lingard, was the best of the lot.
It's easy to forget, considering today's elation, that prior to Stones' opening goal England were sloppy and the defence looked shaky. For example, only two of England's six goals came from the run of play Sunday - as if that sort of thing matters, since set pieces play such a large role in big tournaments.
World Cup - Group G - England vs Panama - Nizhny Novgorod Stadium, Nizhny Novgorod, Russia - Jun 24, 2018 England's John Stones celebrates scoring their fourth goal with team mates.
Lingard bends in a beauty in from distance to make it 3-0 to England. The Manchester United man is quite inexplicably, turning into a force behind Kane and the driver of their attacking quartet.
"I just thought we were a little bit anxious at the start and it was a very hard challenge because [Panama had] six at the back and three in midfield, and they pressed well off of that".
That is the scenario heading into Thursday's clash with Belgium, who would reportedly rather finish as runners-up.
Captain and star striker Harry Kane bagged a hat-trick - taking his tally for the tournament to five - while John Stones popped up with two surprise goals. "What we did was to try to avoid a bigger catastrophe in the second half", Gomez added.More news: Mavs swap picks with Hawks to get Luka Doncic
'I think they can see what we're trying to do and the way we're trying to play and that the players are enjoying their football.
With half-time approaching England became the fifth team in World Cup history to score five or more in the opening period.
The Three Lions controlled the game and had a third goal in the 36th minutes as Lingard made a right footed shot from outside the box to the top right corner and scored. A former England global, he has been around long enough to know that most of the battle in soccer is creating quality chances, and if a team's players are as world class as England's are, eventually those attempts will start to hit the back of the net.
Senegal and Japan drew 2-2 earlier Sunday and lead the group with four points each.
"The free kick we scored against Panama just shows how imaginative we can be going forward".
Kane was delighted with the way his side advanced from the group with a game to spare and was happy to see the work they have done on set-pieces pay off against Panama.
"I believe I used substitutions very well in looking back", said Japan coach Akira Nishino, who took over shortly before the tournament started.More news: Rudy doubt for Germany with broken nose