Kane, substituted to an ovation from the almost 2,500 England fans, was the third England player to score a hat-trick at a World Cup following Geoff Hurst in the 1966 final and Gary Lineker against Poland in the 1986 tournament.
Sunday's qualification for the last 16 with a game to spare, Harry Kane leading the race for the Golden Boot and a record World Cup win after thrashing Panama 6-1 - England could not have wished for a better start in Russian Federation.
England and Belgium go into their Group G game on Thursday with identical records, meaning the team that receives the most yellow cards could finish as runners-up in the group.
The Tottenham striker bagged his third after a 61st minute shot by Ruben Loftus-Cheek hit his foot and bounced over Panama goalkeeper Jaime Penedo.
Lifting the trophy may well prove to be beyond them, but England have shown there are many bright days ahead for this young side and their manager.
Kane netted two unstoppable first-half penalties before a fortuitous third in the second period to become the first man since former Barcelona and Spurs striker Gary Lineker in 1986 to score a World Cup hattrick.
"I think there's been much less expectation on the World Cup this time, which is probably a good thing". They emulated the feat of Germany's Ottmar Walter and Fritz Walter, brothers incidentally, who scored two goals each during their team's 6-1 win during the 1954 semi-final over Austria.
Japan's Nishino says marking Mane is not the whole answer
ET on Sunday in a crucial game for both sides, after many expected Poland and Colombia would be the teams advancing from Group H . Tunisia forced a 1-1 draw against Belgium in Oita. "We didn't start very well, that's true, and now we have to overcome that".
It remains to be seen if finishing top would even benefit England with Japan on course to claim top spot in Group H and Senegal in second after their 2-2 draw in Ekaterunburg.
Both Cristiano Ronaldo and Romelu Lukaku are in second place with four goals each.
"Scoring two goals is not something I thought I'd do at the start of the game, but it's great to get through".
"With the squad that we've got and confidence flowing, I don't see why we can't go far, but we just want to take it game-by-game".
England's biggest-ever World Cup win, which included two penalties by Kane then a deflection off his heel, also guaranteed Belgium's berth in the next round.
What more could Panama captain and defender Felipe Baloy ask for.
At 9pm (Thailand time) Group A leaders Russian Federation play Uruguay, while Saudi Arabia face Egypt.