We'd had the lion's share of possession in the first half-hour and then hit the Hammers with a one-two in the space of four minutes.
The first goal was a lightning break from Andy Carroll's loose pass, the pace of the transition from Christian Eriksen to Dele Alli to Kane heading home something to behold.
The second goal wasn't far away, created by Jan Vertonghen, Dele denied by Joe Hart and Kane there to roll home the rebound from the edge of the box.
We were well in control and it was no suprise when Eriksen drilled home the third after Kane had struck the post with a free-kick on the hour. The midfielder is now the highest Danish scorer in Premier League history.
West Ham hit back through Chicharito and we heaped pressure on ourselves when Serge Aurier was sent off for a second bookable offence 20 minutes from time.
To be honest, we looked more likely to score on the break but Cheikhou Kouyate headed home three minutes from time to up the ante even more. This time, we stood firm to take a deserved three points.
Mauricio Pochettino made two changes to the team that started against Swansea City last time out in the top flight. Aurier made his full Premier League debut in place of Kieran Trippier while Ben Davies returned for Heung-Min Son. Mousa Dembele missed out with an ankle problem.
GOAL: WEST HAM 0-1 SPURS - HARRY KANE - 34mins
We had the better of it as the teams sparred for the first half-hour - Joe Hart tipped over from Christian Eriksen - before taking the lead on 34 minutes. Andy Carroll looked inside from half-way but his loose pass went straight to Eriksen and we struck quickly. Eriksen went wide right to Dele and his cross was perfect for Kane to stretch and glance a header across Hart into the far corner.
GOAL: WEST HAM 0-2 SPURS - HARRY KANE - 38mins
Our second goal also started with West Ham in possession. This time, Hart kicked long, won by Jan Vertonghen. As the ball came down, Vertonghen took off down the left as Eriksen flicked the ball into his path. The Belgian defender played in Dele, Hart did well to block but the ball ran to Kane, who rolled the ball into the empty net.
Above: Harry Kane tangles with Angelo Ogbonna.
GOAL: WEST HAM 0-3 SPURS - CHRISTIAN ERIKSEN - 60mins
Kane drilled a free-kick from the left corner of West Ham's box beyond the wall and Hart, only for the ball to cannon back off the foot of the post. Play continued, Aurier's cross found Eriksen and the Dane drove low with great technique into the bottom corner.
GOAL: WEST HAM 1-3 SPURS - JAVIER HERNANDEZ - 66mins
A bread and butter response came quickly from the Hammers. Mark Noble curled in a corner from the right, Jose Fonte flicked on at the near post and Chicharito nodded past Hugo Lloris from six yards.
RED CARD: AURIER SHOWN SECOND YELLOW CARD - 70mins
We suffered a jolt soon after West Ham's goal as right-back Aurier picked up a second yellow card in the space of six minutes, the second bookable offence a foul on Carroll. Moussa Sissoko sat in at right wing-back before Kieran Trippier's arrival on 78 minutes.
GOAL: WEST HAM 2-3 SPURS - CHEIKHOU KOUYATE - 87mins
We looked to have weathered the minor storm - indeed, we had chances on the break ourselves, especially Dele breaking from deep - but West Ham pulled a second goal back late on to set up a nervous ending as Kouyate powered home a header from Arthur Masuaku's cross. From there, it was typical derby stuff - we broke and could have scored, West Ham put us under pressure with a couple of crosses and corner, both teams 'got together' on half-way and it finally all ended on 97 minutes!
MAURICIO POCHETTINO SAID
“Our effort was fantastic. We competed, played well, (we were) unlucky in the end because we suffered a little but I'm so happy with the three points. We conceded a goal in a situation we knew well (that) they were strong in that phase of the game and when we played with 10 it was difficult, they started to dominate. Sometimes it’s good to win in that way, fighting, suffering. I enjoyed it. I like to win sometimes in that way because you are more close, the team is with you, the fans, suffering all together, it’s an emotion that makes you stronger."
TOBY ALDERWEIRELD SAID
"I thought we dominated the game and had everything under control. Hugo didn’t have to make one catch until the red card. Then we fought as a team, defended well. It was a good victory, we fought hard for it. The away wins are important, difficult games as well against Newcastle, Everton and West Ham. Now we have to take our points in home games as well. We’ve been playing well and we’ve been unlucky. We’ve dominated the games and if we continue to play well, the points will follow."
West Ham: Hart, Fonte (Masuaku 74), Ogbonna, Reid, Zabaleta, Kouyate, Noble (c), Cresswell, Antonio (Carroll 28), Hernandez, Arnautovic (Ayew 66). Substitutes (not used): Adrian, Rice, Byram, Sakho.
Spurs: Lloris (c), Alderweireld, Sanchez, Vertonghen, Aurier, Dier, Sissoko (Trippier 78), Davies, Dele, Eriksen (Winks 73), Kane (Llorente 89). Substitutues (not used): Vorm, Walker-Peters, Nkoudou, Son.
Goals: West Ham - Hernandez 66, Kouyate 87; Spurs - Kane 34, 38, Eriksen 60.
Yellow cards: West Ham - Hernandez 80, Ayew 90+3, Reid 90+6, Carroll 90+6; Spurs - Aurier 64, 70, Llorente 90+6, Dier 90+6.
Red card: Spurs - Aurier 70.
Referee: Michael Oliver.
MAN OF THE MATCH
With 62 per cent of fans' votes on social media, two-goal Harry Kane was named as Man of the Match.
It's a quick turnaround for the team as we travel to Cyprus on Monday for Matchday Two in UEFA Champions League Group H against APOEL of Nicosia on Tuesday (7.45pm UK). We beat Borussia Dortmund 3-1 in our group opener while APOEL lost 3-0 at Real Madrid.