The striker planted home a header from Eric Dier’s cross in the 24th minute for his 21st goal in the top flight.
An almost textbook away display secured maximum points and with Liverpool losing at Stoke, we leapfrogged the Anfield men into fifth place.
That means we’ll go into the group stage of the Europa League next season.
Mauricio Pochettino was forced into a change in the final match of the 2014-15 campaign as Danny Rose missed the trip to Merseyside through a dead leg. The Head Coach had hinted he may involve Brad Friedel in his last game before his retirement, but a shin injury ruled him out also.
Mousa Dembele came in for Rose as Nabil Bentaleb took the left-back spot, with Dembele anchoring the midfield alongside Ryan Mason.
There was a youthful looking bench too as academy players Harry Winks and Josh Onomah came into the squad.
Erik Lamela has impressed of late and had the first chance of the game inside the opening five minutes when he found a pocket of space just outside the Everton penalty area but lofted his shot over the bar.
We looked bright and sharp in our build-up play early on as we pushed the Toffees back towards their own goal.
Our best chance came in the 17th minute when Christian Eriksen charged down a pass from Brendan Galloway and played in Lamela who was denied only by an excellent piece of goalkeeping from Tim Howard.
For all our dominance we almost fell behind a minute later when Kevin Mirallas sprung the offside trap and raced through on goal but saw his shot smothered by Hugo Lloris.
The three behind Kane looked a constant threat with Eriksen finding time and space at will and it was the best away performance since the second half at Newcastle. That was the last time Kane found the net and he duly broke the deadlock with 24 minutes played.
Mason turned a clearance into the path of Dier who whipped in a perfect cross first time for the striker to glance a header past Howard and give us the lead.
It was one-way traffic after that, although Mirallas almost found a leveller in the dying moments of the half when he drew Lloris from his goal and lobbed the ball back over him - his effort landing on the roof of the net.
On balance our lead probably deserved to be greater although Roberto Martinez’s side came out with more purpose in the second period.
We had Lloris to thank in the early stages of the second half when he dived bravely at the feet of Galloway.
We appeared to weather the early storm after that as we retained the ball for long spells. Eriksen forced a succession of corners and Mason kept things ticking.
Chances remained at a premium but our fans continued to make plenty of noise in the corner of Goodison Park as the sun shone brightly on Merseyside.
Everton substitute Steven Naismith went closest in the latter stages with an overhead kick but we saw the game out to claim the points and end the season on a winning note.
Everton: Howard, Coleman, Galloway (Distin, 84), Stones, Jagielka, McCarthy, Barry, Mirallas (Naismith, 73), Barkley (Besic, 45) Osman, Lukaku. Substitutes (not used): Robles, Atsu, McGeady, Kone.
Spurs: Lloris (c), Dier, Fazio, Vertonghen; Bentaleb, Dembele (Stambouli, 53), Mason, Chadli (Soldado, 90+3), Lamela; Eriksen; Kane (Townsend, 84). Substitutes (not used): Vorm, Yedlin, Onomah, Winks.
Goals: Spurs - Kane (24).
Yellow cards: Everton - Jagielka. Spurs - Stambouli, Mason.
Referee: Jonathan Moss.