Kane set up Son Heung-min to open the scoring in the first minute at Tottenham Hotspur Stadium with a fine long pass.
The England striker then scored two of his own in the next quarter of an hour, drilling an effort beyond Lukasz Fabianski from the edge of the box before heading in a pinpoint cross from Sergio Reguilon.
Spurs' flying start saw Kane reach 12 goal involvements (five scored, seven assisted) in his first five matches of the 2020-2021 league season. No player has ever managed as many in their opening five games of a campaign in the Premier League era, with the previous best of 11 set by Thierry Henry for Arsenal in 2004-2005.
The 27-year-old has been involved in a remarkable 23 goals in his most recent 12 competitive outings for Spurs, scoring 15 and assisting eight. He has managed at least one goal and one assist in each of his past three games.
Kane and Son's partnership continues to flourish. They have combined for 28 goals in the Premier League, the fourth most of any combination in the competition's history and only six goals behind record-holders Frank Lampard and Didier Drogba (36).
The duo have thrived under Jose Mourinho. Since he took charge last November, Kane (33) and Son (30) have had a direct hand in more goals in all competitions than any other players in England's top tier.