The Cherries got off to a blistering start, with Junior Stanislas drilling in the seventh-minute opener moments after hitting the crossbar.
And it got worse for Spurs as top scorer Kane was forced off with an ankle injury after he collided with Asmir Begovic.
But Dele Alli equalised from Serge Aurier's cross soon after.
Son won the match with two second-half goals, before Aurier wrapped up the victory with a stoppage-time header.
Spurs are a point above fourth-placed Liverpool. AFC Bournemouth remain 12th.
AFC Bournemouth: 17 Mar v West Brom (H)
Tottenham Hotspur: 1 Apr v Chelsea (A)