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.
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.
Kane's hat-trick was completed in freakish fashion in the 62nd minute after a Ruben Loftus-Cheek deflected off the English captain's heel into the net.
Legend Geoff Hurst was the hero on that occasion, scoring a hat-trick in England's most famous triumph.
On the prospect of winning the Golden Boot, Kane said: "There's still a long way to go. You don't get many opportunities to play in a game like that for England".
England manager Gareth Southgate has heaped praise on the Russian Federation 2018 World Cup infrastructure and stadiums and admits he and his team have "been really looked after" in the country. "He's not just a player that stands up front and waits for chances and that's important within the ethic of the team we're trying to create".
"I don't know how Gareth could send those lads out there and say, "We need to get a draw today" or "We need to get more yellow cards".
"It's one to be proud of", he said of the adidas Telstar 18.More news: North Korea sanctions to remain until denuclearization achieved - S. Korea
"I'm happy with how I played".
Southgate's task now will be to keep his young charges' feet on the ground, and guard against complacency whomever they face next from Group H's quartet of Japan, Senegal, Poland and Colombia.
"We would want to keep momentum and keep progressing as a team", Southgate added.
World Cup Daily: England shrug off years of mediocrity while Poland fail to impress.
"I was pleased the captain got his hat-trick because it meant he had the hump less when I brought him off!" quipped Southgate.
# This is only the fifth time in World Cup history that a team has scored 5+ goals in the first half of a match, with Germany vs Brazil in the 2014 semi-final the most recent occasion.
"They have some outstanding individual players", he said.