Kane struck from close range in the 59th minute for his second goal in successive league games, but injured his right ankle in the closing minutes and left the stadium on crutches.
Adnan Januzaj made a similar journey moments later after the Sunderland winger, on loan from Manchester United, was sent off for his second yellow card, an ugly studs-up lunge on Ben Davies. In truth, Sunderland got what they deserved – nothing – from a game in which they showed little ambition and were second best throughout.
Tottenham, by contrast, are still unbeaten and quietly carrying on where they left off last season. They may have scored only one goal, but the statistics paint a truer picture, with Tottenham’s total of 31 efforts far superior to the six of Sunderland.
“Our passion and attitude was fantastic and I am disappointed it was only 1-0,” Mauricio Pochettino said. “But it is an important three points for us to stay at the top. I’m happy Harry scored but disappointed about his injury. We’ll assess his ankle on Monday.”
Patrick Van Arnholt was withdrawn shortly before kick-off despite being named in the Sunderland starting line-up. Pictures showed the left-back looking baffled when he was told in the warm-up that he would not start, and David Moyes was cagey with his response to questions about the switch. “I’ll give my stock answer which is that it was for medical reasons, and I don’t want to say more.”
Van Arnholt was replaced by Jason Denayer, who was given a torrid afternoon by Heung Min Son, the Korean striker who has been in fine form since failing to get a move back to Germany in the summer.
It was evident from the start that Tottenham would be doing all of the attacking and Sunderland would hope to hang in there and try to score on the counter-attack.
Pochettino changed his team from the one that lost to Monaco in the Champions League on Wednesday, with Mousa Dembele starting for the first time after a six-game suspension.
Dembele was the hub of Tottenham’s best football as they created chance after chance, only to be thwarted time and time again by Jordan Pickford in the Sunderland goal.
The young keeper was excellent throughout, making important saves as Spurs struggled to break through. Dembele, Kane, Toby Alderweireld and Victor Wanyama were all denied in the opening 15 minutes, which resembled a training ground exercise with visitors camped deep in their own half.
Sunderland’s only decent chances fell to former Spurs Jermain Defoe, whose shot was saved, and Steven Pienaar, whose effort was cleared off the line by Kyle Walker.
At the opposite end, Son struck a post from 20 yards, then shot over the bar and hit the side-netting from close range.
Tottenham finally broke through after 58 minutes. Walker curled in a deep cross from the right, Dele Alli directed his header towards Papa Djilobodji, who controlled the ball but lost his footing leaving Kane the simple task of sliding the ball home from six yards.
Spurs are now four points behind Manchester City, who visit White Hart Lane in a fortnight’s time, and Pochettino says they can cope if Kane is out for an extended spell. “That is why we signed Janssen. We have plenty of options,” he added.
Lloris 6; Walker 7, Dier 6 (Davies 77), Alderweireld 7, Vertonghen 6; Wanyama 6, Dembele 7 (Lamela 74); Sissoko 6, Alli 7, Son 9; Kane 7 (Janssen 87)
Vorm. Trippier, Winks, Eriksen
Pickford 8; Denayer 4 (McNair 90), Kone 6, Djilobodji 4, Manquillo 6; Januzaj 5, Kirchoff 6 (Khazri 78), Cattermole 6, Pienaar 5 (Watmore 62); Ndong 5; Defoe 6 Subs not used: Domingues, O’Shea, Gooch