Javier Hernandez pulled one back for West Ham after Christian Eriksen had made it three, but despite Sergie Aurier picking up a red card and Cheikhou Kouyate netting late on, the hosts were unable to stage a comeback.
West Ham looked slightly more threatening in the early stages, with Hernandez seeing a hopeful effort from distance palmed over by Hugo Lloris and Marko Arnautovic being thwarted by a last-ditch tackle from Aurier in the box.
The first real clear-cut chance did not come until the 34th minute and Tottenham made it count, with Dele Alli running onto Eriksen's ball before picking out Kane in the middle to head home.
And the home side were given a further boost five minutes later when Tottenham were reduced to 10 men after Aurier was shown a second yellow card for a late tackle on Andy Carroll.
West Ham pulled another back with just a few minutes left on the clock when Kouyate arrived at the far post to head in Arthur Masuaku's cross, but Spurs were able to hold on for the three points.
- West Ham 2 Tottenham 3: Harry Kane hits double as Spurs cling on for win after ...Evening Standard
- Tottenham star Harry Kane is now the king of London derbies... but Dele Alli ...Daily Mail
- West Ham 2 Tottenham 3: Spurs head off West Ham fightback as Harry Kane wins ...Telegraph.co.uk
- West Ham vs Tottenham live score: Premier League goal updates and team newsEvening Standard
- West Ham 2-3 Tottenham LIVE score and goal updates as Christian Eriksen and ...Mirror.co.uk
- Serge Aurier's kamikaze red card didn't cost Tottenham at West Ham... but the ...Daily Mail
- Premier League table: How the standings look after Tottenham beat West HamExpress.co.uk
- Harry Kane brace sees Tottenham Hotspur beat West Ham United in Premier LeagueHindustan Times
- West Ham transfer news: Slaven Bilic reveals Andy Carroll must prove fitness ...The Sun