The Tottenham striker netted the Three Lions' second goal from the penalty spot and then, in a remarkable half of football, also scored England's fifth in a completely one-sided 45 minutes.
Both goals came from the penalty spot, following Panama's rough-housing tactics at corner kicks.
Kane subsequently becomes the first Englishman since 1990, after David Platt and Gary Lineker, to score three goals at the competition.
He is also the first ever player to score four goals in a World Cup group stage, topping Lineker's three in 1986, and Roger Hunt's in 1966.
The first penalty was, remarkably, the first England have scored in open play at a World Cup since 2002, when David Beckham netted against Argentina.
The second from the spot saw him become the first player in 44 years to score two goals in each of his first two World Cup games.
2 - Harry Kane is the first player to score a brace in his first two World Cup appearances since Poland's Grzegorz Lato in 1974, who went on to win the Golden Boot at that tournament. Talisman. #ENGPAN #ENG #WorldCup pic.twitter.com/yY4el9eGJb— OptaJoe (@OptaJoe) June 24, 2018
John Stones scored the first and fourth goals - becoming the second Manchester City player to score at a World Cup, after Trevor Francis in 1982, with Jesse Lingard curling a brilliant strike home from outside the box.
5 - 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. Rout. #ENGPAN #ENG #WorldCup pic.twitter.com/dM69aHGaqh— OptaJoe (@OptaJoe) June 24, 2018
England have never scored five goals at a World Cup before, and the statistic becomes even more remarkable when it is considered that the goals were scored across 45 minutes, at a rate of one every nine minutes.
Furthermore, England have eclipsed Euro 2016's total of four goals, in one half of football.