Kane was a constant menace and he went close with a curling effort before underlining his predatory excellence in the 25th minute.
Jan Vertonghen's long pass targeted a penetrating run from Son and, with Leicester caught flat-footed, the South Korean quickly picked out Kane, who arrived on cue to guide a clinical finish past Schmeichel from close-range.
Although Leicester had a penalty appeal rejected after Toby Alderweireld collided with Vardy, Tottenham were proving impossible to subdue and the visitors doubled their lead in the 36th minute.
Alli was the catalyst, taking possession on the edge of the area and impudently bypassing the Leicester defence with a sublime chipped pass to Son, whose half-volley lacked power but still had enough accuracy to beat Schmeichel.
Son's 20th goal of the season was just reward for Tottenham's dominance, but Leicester got one back in 59th minute.
Despite replays showing he was marginally offside, Vardy was allowed to sprint onto a through ball, prompting Lloris to rashly race well outside his area in a failed attempt to clear.
When Daniel Amartey poked the ball to Chilwell, the Leicester defender steadied himself before firing home via Eric Dier's out-stretched foot.
Even that needless setback couldn't ruffle Tottenham and they responded with a well-worked third goal four minutes later.
Alderweireld looped a cross into the Leicester area and Victor Wanyama nodded back towards Kane, who reacted quickest to head in from close-range.
Kane turned provider for Tottenham's fourth goal in the 71st minute as his pass teed up Son to flash a fine finish past Schmeichel.
With Leicester's minds turning to their post-season holidays, Kane had acres of space to pilage the hosts' defence and he completed his hat-trick with a superb 20-yard strike in the 89th minute.
Kane wasn't finished yet and he produced a carbon copy of his third goal in stoppage-time, driving home from the edge of the area to put the seal on his goalscoring masterclass.