Kane headed Erik Lamela’s pass into the path of Son, who headed home Spurs’ first effort on target.
That is the 29th time the pair have combined for a Premier League goal, while Son is now the division’s leading scorer with eight.
Burnley were unfortunate to lose with Ashley Barnes having a goal ruled out for offside and Kane clearing a James Tarkowski header off the line.
Ashley Westwood and Johann Gudmundsson also forced Hugo Lloris into saves.
Sean Dyche’s Clarets remain in the relegation zone on one point, while Spurs move up from 11th to fifth.
Son and Kane’s productive partnership
Son and Kane have had a good partnership in recent years but this term they seem to have taken it to near telepathic levels.
They have linked up for four goals against Southampton, two against Manchester United and West Ham and now another against Burnley.
Kane appeared to know Son would be there when he flicked Lamela’s corner on and the South Korean made no mistake as he threw himself at the ball to head in.
He is now the top scorer in the league, while Kane – who has five goals and eight assists – has been directly involved in 13 goals, the most ever recorded by a player in his team’s first six Premier League games.
They have linked up 29 times for league goals in total. Only Chelsea’s Didier Drogba and Frank Lampard (36) have ever managed to do so more often.
Spurs and boss Jose Mourinho will be happy that is the focus of the game, because they had been poor otherwise.
They were sloppy in possession, gifting Burnley several chances with defensive mistakes – and barely created a chance before Son’s goal.
Kane’s main role until then had been to clear a Tarkowski header off his line.
Spurs are the top scorers in the league – they were averaging three goals a game until Monday night’s match – but had perhaps taken criticism of their last league game to heart.
They led that one 3-0 against West Ham after 16 minutes before conceding three times in the final eight minutes to draw 3-3.
There was no danger of such drama this time.
Positives to take… but it’s another slow Burnley start
Burnley struggle at home against the big sides, despite their reputation for being difficult opponents. Their only win in their past 24 Premier League home fixtures against ‘the big six’ came last season against Spurs.
They are traditional slow starters. They have failed to win in their opening five Premier League games twice before, in 2014-15 when they had three points and in 2018-19, when like this year they picked up one point.
They were relegated in 2015 and stayed up by six points two years ago.
The Clarets will have to start picking them up soon as they are level on points – well point – with Sheffield United and Fulham in the relegation zone.
Burnley boss Dyche will see the positives from this performance though and on another day they could have scored a couple.
Barnes was well offside when he slammed home in the first half and they forced Lloris into three saves and Kane into his clearance.
They were solid at the back for the most part too, with Kevin Long doing well to block a Son effort and Tarkowski denying Kane.
Match stats – Mourinho’s favourite opponents
- Tottenham recorded clean sheets in successive games in all competitions, having failed to record a shutout in 10 games stretching back to last season.
- Jose Mourinho has not faced any side as manager more often without losing than Burnley (10 – W6 D4), winning five of his six away matches against the Clarets.
- Tottenham have lost just one of their past 12 Premier League games played on Monday (W9 D2), going down 1-0 against Man City in October 2018.
- Harry Kane has recorded eight assists in six Premier League appearances this season, the most he has ever provided in a single campaign in the competition.
- Josh Brownhill’s booking for Burnley after 63 seconds was the earliest in a Premier League game since Scott McTominay for Manchester United against Newcastle in December 2019 (24 seconds).
Burnley host Chelsea in the league on Saturday (15:00 GMT). Spurs go to Belgium to face Royal Antwerp in the Europa League on Thursday (17:55) before a home game against Brighton in the Premier League on Sunday (19:15).