Jose Mourinho's side bounced back from a disappointing opening game defeat against Everton by securing a 5-2 victory at St Mary's, with Son grabbing the first four goals of the game before Kane rounded off the scoring.
Southampton took the lead in the contest 32 minutes in through Danny Ings, but Son latched onto a perfectly weighted Kane pass to hit an equaliser right on half-time, sparking a significant momentum shift.
The South Korea international grabbed his second with another expert finish just after the restart, and completed his hat-trick just past the hour after latching onto another incisive through ball from Tottenham's No.10.
Son went on to grab his fourth after being set up by Kane once again, before the England international got his name on the scoresheet with eight minutes left to play.
Ings notched his second goal of the game in stoppage time, but it proved to be nothing more than a consolation for a Southampton side who are now winless after their first two fixtures of the new campaign.
Kane laid on all four of Son's goals against the Saints, becoming the first man to assist the same player four times in a single match in the Premier League era.
4 - Harry Kane has assisted all four of Son Heung-Min's goals against Southampton today - the first time in @premierleague history one player has assisted another four times in a single match. Fabulous. pic.twitter.com/EloGFWjEyE— OptaJoe (@OptaJoe) September 20, 2020
The Spurs frontman is the first English player to have ever assisted four goals in a Premier League fixture, and the sixth to achieve the feat in the competition's history.
Kane is also the first man to have been directly involved in five goals since Mohamed Salah in March 2018, when the Liverpool forward grabbed four goals and an assist to inspire a 5-0 win against Watford.
Meanwhile, Son's treble marks only the fourth time a player has scored a top-flight hat-trick with one player assisting each goal, and he and Kane have linked up to score a total of 24 goals between them since 2015, more than any other duo during the same period.