Spurs doubled their lead two minutes into the second half as Son turned provider to pick out Kane, who made no mistake from close range, 2-0.
Tottenham are three points adrift of Jurgen Klopp's men following a decent return during the festive schedule.
Early and often the signs pointed to an eventual Tottenham opener. More slick play from Spurs.
All 11 players were up for this match; that was apparent from kick off.
Wayne Rooney had the ball in the back of the net seven minutes later but it was ruled out for offside.
This game should be a far more open affair, allowing Tottenham's attack to trouble Everton's defensive frailties.
Son was not to be denied four minutes later when the South Korean was on hand to turn home Serge Aurier's cross.
With Harry Kane in town, this is an issue that Everton must address, or they run the risk of being embarrassed by the Tottenham forward.
But the Blues could not pierce Leicester's defence at Stamford Bridge even when visiting left-back Ben Chilwell was sent off for a second bookable offence midway through the second half. He spun on a dime in the 47th minute to leave his mark in the dust and smartly, if not inadvertently, whipped the ball into Kane's path, who was left with the easiest of tap ins. Son cuts in from the right and thunders a superb strike against the post. Everton were outclassed in every facet of the game, highlighting what was a flawless home outing. Christian Eriksen rounded off the scoring for the host in the 81st minute.
Admittedly, Everton are plagued by numerous pervasive inflictions, including their inability to muster any offence whatsoever.
The Spurs striker, who hit 56 goals in 2017 - more than any other player in Europe's top five leagues - has been consistently linked with moves away from the club, with Real Madrid reportedly keeping tabs on his availability.