The PFA Young Player of the Year headed Eric Dier’s 24th-minute cross beyond Tim Howard, meaning Everton missed out on the top 10 just one year on from their fifth-placed finish in Roberto Martinez’s maiden campaign.
Spurs started brighter and claimed a deserved lead when Kane stooped to connect with Dier’s inviting first-time delivery, guiding his header beyond Tim Howard for his first goal in five matches.
The Toffees stirred after the break as half-time substitute Muhamed Besic steered a long-range try wide, Leon Osman volleyed off target and Galloway almost broke beyond Lloris.
Spurs settled back into their pattern of dominating possession while their lacklustre hosts ambled around the pitch.
Kane’s blushes were spared by the offside flag as he headed a simple chance wide, after Eriksen clipped the ball into him.
Sylvain Distin appeared for a farewell cameo for Everton near the end.
However, his arrival, and the Liverpool result, produced the only cheers of the afternoon from the home faithful.
Howard, Coleman, Stones, Jagielka, Galloway (Distin 84), McCarthy, Barry, Mirallas (Naismith 73), Barkley (Besic 46), Osman, Lukaku.
Lloris, Dier, Fazio, Vertonghen, Bentaleb, Dembele (Stambouli 53), Mason, Lamela, Eriksen, Chadli (Soldado 90), Kane (Townsend 85).