England made light work of a Panama side focused on unsettling rather than outplaying them, with captain Kane becoming his country's third player to score a World Cup finals hat-trick when the ball went in off him early in the second half.
It was the first time England have scored more than four goals in a single game at a World Cup, and they will now play off with Belgium to decide who will top Group G.
Kane netted a hat-trick as England recorded their highest-ever World Cup goals tally - and biggest-ever World Cup winning margin - in a rout against debutants Panama to book their spot in the last 16 in Russian Federation with one game to spare.
When asked what scoring sensation Kane's World Cup appearances would mean for a potential big-money move away from Tottenham, Schmeichel suggested Kane would not be a in a hurry to leave White Hart lane. They have already scored twice as many goals.
The most important thing is that my goals help my team win.
Belgium boss Roberto Martinez has admitted he is tempted to make alterations to his side and rest key players, while England's Gareth Southgate could yet follow suit. The most important thing is winning games, and if my goals help my team win then that's the ideal situation.
Turquie: Erdogan réélu pour un mandat aux pouvoirs renforcés
Au pouvoir depuis 15 ans, Recep Tayyip Erdogan n'a pas attendu l'annonce de la commission électorale pour revendiquer la victoire. Erdogan est arrivé en tête de la présidentielle avec un score de 52,5 % après dépouillement de plus de 99 % des urnes.
Panama got themselves into good positions on a number of occasions, however, it was England who would score again on 22 minutes, courtesy of yet another World Cup 2018 penalty.
"You think back to the last World Cups, where we drew 0-0 with Algeria and struggled to score against United States of America, and we look much better", he tells Newsbeat.
In England's 6-1 demolition of Panama on Sunday, their last goal was preceded by 25 passes. Kane nods it to Sterling, whose header is deflected by the 'keeper into the path of Stones, who gets his second of the day!
"Football's coming home" rang out at the final whistle, with Southgate forgetting his dislocated shoulder to celebrate wildly with England's travelling support.
Finishing top of Group G would bring a possible quarter-final against Brazil or Germany, while the runner-up would potentially go on to face Mexico or Switzerland.
England showed no mercy and a smart set-piece routine saw Jordan Henderson clip a first-time ball over to Kane, whose header across goal was met by Sterling.
Edu del prado d'"Un, Dos, Tres" est décédé
Edu del Prado était aussi l'un des talents de The Voice en France et il avait choisi le morceau de Beyonce " Listen ". Tantos recuerdos en mi corazón, lo conocí con 11 años en mi proyecto Tattoo, él ya era un ídolo con su primer disco.
The fifth goal came shortly before half time, when a catalogue of fouls in the box could have earned England their second penalty.
With five goals in two games in his World Cup debut, Kane is the leading scorer at this year's tournament - one ahead of Portugal's Cristiano Ronaldo and Belgium's Romelu Lukaku.
England made it 3-0 in the 36th minute, with Lingard producing a gem of a finish.
"I'm insane about this guy, he is top, top class", former Denmark 'keeper Schmeichel said of Kane, who is now the outright top-scorer at Russian Federation 2018 with five goals to his name.
Kane scored another penalty just before halftime. England must hope that Dele Alli recovers from injury to resume his role in Kane's back.
"I just thought we were a little anxious at the start".
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Quatre jours après le match, le technicien français n'a toujours pas digéré les "faits de jeu qui se sont produits contre le Portugal ".
If they do end up atop the group, then it is hard to discount their chances in the knockout stage as momentum plays a big part in a competition like the World Cup.