Kane's third successive victory is the fifth consecutive season in the Premier League, compared to Andy Cole and Steven Gerrard.
Christian Eriksen and Son Heung-Min have added extra points as Spurs won in the second half and came in second place, above Manchester City, and six leaders Liverpool.
The Italian side seems likely to have Mauricio Pochettino still absent from the Premier League, as well as against Wolverhampton Wanderers.
They played for Cardiff in a few minutes, and the third goal hit the game, with & # 39; Ole & # 39; from the fans who visited after half an hour.
Cardiff's disappointing record for the top clubs continues, having lost in their last 15 Premier League meetings against United States and six in 39 teams, scoring 45 goals.
Bluebirds have picked up four points from their last two encounters and found the net after five points clear of Manchester United in the first leg of their home tie, but hope for a three-match unbeaten run disappeared.
Kane's shot came in from the referee and Cardiff's Sean Morrison captained Kieran Trippier to the right on the right after attacking England's captain.
The England striker has now scored 16 goals in his last 12 Premier League appearances against new clubs.
Spurs made just 2 minutes to 12 minutes with the winner against Eriksen.
The midfielder signed for Bruno Ecuele Manga and Harry Arter in the middle of the pitch before pulling off his left foot in the box, and featured in Moussa Sissoko and Son.
The boy finished 3-0 at the end of the game, while South Korea later delayed Kane's late penalty, while Morrison pounced before heading to Neil Etheridge's corner and his 11th goal of the season. the last game.
The arrival of Junior Hoilett, who was substituted by Cardiff's youngest player, gave Spurs something to think about in the second half.
The winger saved two goals from Hugo Lloris, the first time he headed home, leading to a bust-up and a frustrating start to his career.
Cardiff faced difficulties in the 59th minute when Victor Camarasa scored the winner against Leicester on Saturday, suffering a knee injury against Joe Ralls.
Spurs looked at the other side and Kane threatened again for an hour after scoring and drawing up after Dele Alli's move.
Then the boy refused to go to Etheridge after Kane scored the goal.
Cardiff has never been involved, Lloris has taken over from Aron Gunnarssson, but there is no quality Spurs quality.