The forward scored his side's second goal in a 5-0 routing of Southampton on Sunday night, a result that left Spurs in 10th place with 23 points after 16 matches.
The 32-year-old also registered two assists, the first of which came in the 25th minute for Pape Matar Sarr and brought Son level with Anderton's total of 67 Premier League assists.
Son overtook Anderton just before half time when he released James Maddison into the penalty area, and in turn claimed a record that had stood since 2004.
There have been some question marks about whether the Spurs captain would be able to continue performing at a high level into his thirties, but he proved on Sunday that he can still significantly impact games.
Could Son break more records?
Son has also made 300 appearances for Spurs in the top flight and it is possible that he could make the most Premier League appearances for the club should he stay long enough to overtake Hugo Lloris's record of 361 appearances.
The forward's tally of 125 Premier League goals is the joint 18th highest figure of all time, and he needs just three more to surpass Jimmy Floyd Hasselbaink to claim 16th spot in the all-time scoring charts.
In regard to Spurs, Son's tally of 168 goals for the London side is already the fifth most in the club's history, and is just six fewer than fourth-placed Martin Chivers's tally.
It is difficult to envisage him catching Bobby Smith, who scored 208 goals for Spurs, let alone leading goalscorer Harry Kane, who has netted 280 times for the club.
Son is contracted to stay in North London until the end of this season- though Tottenham have an option to extend his stay with the team until the summer of 2026 - but he has already established himself as one of the club's greatest ever players, regardless of when his time with the side comes to an end.
Written by
Lewis Nolan