Kane scored his first goal after less than a minute and struck again in the 16th to become the Premier League's leading scorer with 21 goals. Christian Eriksen got the third after 52.Tottenham is six points clear of third-place Arsenal and has seven matches left to overhaul Leicester which is in clear sight of a shock Premier League title only a year after facing relegation.
Tottenham manager Mauricio Pochettino told Sky Sports: "We are very calm."
His side was in complete control through the match at White Hart Lane.
Dele Alli, Eriksen and Danny Rose all had chances and Alli had the ball in the net only for it to be ruled out for offside.
Tottenham immediately went ahead when Kane turned in Kyle Walker's cross from the right.
The dominant host doubled its lead in the 16th with Kane's low shot past Bournemouth goalkeeper Artur Boruc after Alli slid a ball through.
Tottenham had a goal disallowed when Alli fired into the net but Kane had been offside when he flicked the ball on.
It got a third goal seven minutes after halftime when Eriksen drove home the rebound after Boruc palmed out Kane's fierce drive.
Kane has been linked with Real Madrid despite the striker signing a new five-year deal in February.
"He is a fantastic player," said Pochettino. "He showed his quality, I am very pleased he is with us."
Defeat snapped Bournemouth's run of three straight wins leaving the team 13th in the standings, 12 points above the relegation zone.
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