Spurs opened the scoring through Kane, capitalising on an error as the front three combined well for the England striker to nod home.
He then put Spurs 2-0 up, as Dele Alli’s shot rebounded to the forward who has clearly put his August blues behind him.
Christian Eriksen then got in on the act, smartly finishing a half-volley as he became Denmark's top scorer in the Premier League.
Javier Hernandez gave the Hammers a lifeline with a header after the hour mark before Cheikhou Kouyate headed home to set up a stunning finish to the game.
Spurs frustrated early
West Ham interestingly lined up in a 5-2-3 system. Swansea City, Burnley and Chelsea all had success clogging the central areas against Spurs, but the Hammers opted to go with just two central midfielders.
The opening stages didn’t bring many chances though, as Javier Hernandez and Eriksen tried from range but neither goalkeeper were particularly troubled.
Marko Aranutovic was almost through on goal, as West Ham countered, Serge Aurier initially missed his interception but recovered exceptionally well to dispossess Arnautovic who would have been one-on-one with Hugo Lloris.
Spurs were clearly frustrated early on, forcing long-range efforts from Eric Dier and Toby Alderweireld. They were missing Moussa Dembele as the front three struggled to receive the ball, prompting Eriksen to drop deeper in possession than he would like.
Antonio off, Carroll on
Injury forced the Hammers into subbing Andy Carroll on for Michail Antonio after 28 minutes. Until this point, the home side looked good on the counter with a quick front three but then had to change their style to accommodate a target man.
After West Ham’s success countering, it was Tottenham who scored the game’s opening goal from a counter-attack.
Carroll gave the ball away to Eriksen in a dangerous area, who freed Alli in the channel who put the ball on a plate for Kane to score his 10th goal in his last five Premier League away games.
Minutes later he then doubled his and Spurs’ tally, scoring his seventh goal in his last six games against West Ham.
Jan Vertonghen freed Alli in the channel, who had his shot saved by Joe Hart but only to fall to a grateful Kane who passed the ball into an empty net.
Spurs were then in cruise control. West Ham’s main outlet in Antonio was subbed off, and the threat of a counter-attack began to diminish as the once loud roar of the Hammers faithful turned to a sea of claret and blue shirts making their way to the concourse early for half-time.
Perhaps Slaven Bilić should have brought Andre Ayew on instead of Carroll, which would have kept the shape that served them well in the opening 28 minutes.
West Ham pushed for a goal but came undone
West Ham’s best chance of creating something had come through Arnautovic, as Aurier looked unsure of his positioning several times but also had the pace to make up for it.
However the more West Ham pushed to get one back, more space opened up for Alli, Eriksen and Kane on the counter at the other end.
Kane then came centimetres away from scoring his hat-trick, taking charge at the free kick but his effort slammed off the post.
From the resulting set-piece, Aurier’s deflected cross found its way to Eriksen who placed the ball in the bottom corner on the half-volley.
That goal saw Eriksen become the Dane with the most Premier League, surpassing former Arsenal striker Nicklas Bendtner.
Kane then hit the other post as Tottenham went through the gears, taking on Winston Reid before firing quickly before Hart tipped the shot onto the woodwork.
West Ham given hope
It could have came 10 minutes earlier, but Hernandez gave West Ham a lifeline as he nodded home from Jose Fonte’s flick on at the corner.
He then almost had another minutes later, a good cross from Mark Noble found Hernandez in the area again getting his head to the ball but Hugo Lloris was equal to the effort.
West Ham had reason to be even more hopeful of a comeback after Aurier was sent off for a second yellow, for a silly challenge, the latest of poor decisions on his first Premier League start.
Hernandez kept knocking on the door, and had a second bite of the cherry but his effort was fizzed straight at Lloris.
Kouyate then set up a frantic finish to the game, meeting Arthur Masuaku's cross at the far post with a thumping header.
Reid volleyed over from a corner and Carroll claimed for a penalty late on but Tottenham held on for the three points.
A late scuffle between Reid and Fernando Llorente marred the end of the game, which is par for the course when it comes to this fixture.