Kane took his league tally to 19 for the season with a goal in each half as second-placed Tottenham moved on to 56 points from 27 games. Chelsea, who have 63, visit West Ham United on Monday.
Little of note happened for the opening 20 minutes before Kane let fly from 25 metres to beat Joel Robles.
He struck again 11 minutes after halftime to take his tally to 14 goals in his last 12 matches in all competitions and eight in his last four, including two hat-tricks.
Romelu Lukaku gave Everton hope in the 80th minute with his 18th league goal of the season before Dele Alli restored Tottenham's two-goal lead in stoppage time.
There was still time for Enner Valencia to score again for Everton but they could not deny Tottenham a ninth consecutive home league victory.
Enter a name and e-mail address and we will e-mail this website link too them.