The South Korea international netted a double for Spurs and laid on another for Harry Kane as the visitors ran out 6-2 victors at Goodison Park.
Kane netted a double of his own, with Dele Alli and Christian Eriksen capping off the final win which takes the north Londoners within six points of leaders Liverpool.
But thrusting themselves into the title picture was not the only achievement to take from the afternoon on Merseyside.
Twenty-six-year-old Son led the way with two goals and an assist, meaning he has contributed to 51 goals in the English top flight since arriving from Bayer Leverkusen in the summer of 2015.
In 112 appearances, Son has scored 35 times and laid on 16 for his Tottenham teammates, to underline his status as a front-line star of Pochettino's side.
That was not the end of the landmarks reached by Tottenham's players on a thoroughly successful weekend, as they extended their lead over fourth place Chelsea to five points.
England captain Kane went to 11 Premier League goals for the season, scoring in the ninth different match of the 2018-19 campaign.
Only Mohamed Salah of league leaders Liverpool has netted in as many separate games this term.
4 - Harry Kane has become only the second player to score 2+ goals in four consecutive Premier League appearances against a single opponent, after Michael Owen against Newcastle United (Aug 1998 to May 2001). Bracing. #EVETOT pic.twitter.com/4auUYAG3so— OptaJoe (@OptaJoe) December 23, 2018
Furthermore, the former Millwall and Leicester loanee became only the second player to score two or more goals in four consecutive top flight appearances against a single opponent.
Only Michael Owen's run against Newcastle during his days with Liverpool rivals the latest record registered by Kane.
9 - This is the 9th different Premier League match that Harry Kane has scored in during 2018-19; the most in the competition alongside Mohamed Salah. Collection. pic.twitter.com/FpPona5BsF— OptaJoe (@OptaJoe) December 23, 2018
Goal of the afternoon went to Eriksen, whose rasping strike extinguished any hope of a second half Everton comeback.
And since the Denmark international arrived in England in August 2013, no player has scored more goals from outside the penalty area in the Premier League.
He surpassed Philippe Coutinho with his 18th goal from range, as Tottenham kicked off the festive period in ideal fashion.