Son set up Kane for Spurs fourth goal of the night and the Englishman's second in a runaway win against Crystal Palace on Sunday to give the duo 14 goal combinations so far this season.
The pair have overtaken Alan Shearer and Chris Sutton, who scored 13 goals at Blackburn Rovers during the 1994-95 season.
"If the stats I was given are correct -- 100 goals scored in the season -- which for a very defensive team, a very negative team, is not bad," Spurs boss Jose Mourinho told reporters after the win against Palace.
Tottenham have a Europa League last 16 tie against Dinamo Zagreb on Thursday and then a north London derby against Arsenal. There is also a League Cup final to look forward to as Tottenham's season comes back to life.
"It was a good week for us. Three matches, nine points, and for next week when we play a crucial match in the Europa, and against Arsenal, nothing could be better for us than to win nine points this week," Mourinho said.
"It is incredible to score four in the Premier League," Son said after the match. "Four amazing assists from Harry, he deserves the man of the match award.
"We have been working for five seasons together now. We know what we like and work hard on our relationship on and off the pitch. Hopefully, there are many more goals to come."
Kane has been at Tottenham his whole career, having progressed from the club's academy, while Son joined the north Londoners in 2015 from Bayer Leverkusen.
Shearer and Sutton's record was close to being broken at the end of the 2018-19 season by then Bournemouth forwards Callum Wilson and Ryan Fraser, who combined for 12 goals with two games remaining, but failed to match the record.