Harry Kane opened the scoring after just 44 seconds as we got off to an ideal start, with the striker doubling his tally a quarter-of-an-hour later.
Christian Eriksen completed the scoring seven minutes after half-time after Kane's drive was parried by goalkeeper Artur Boruc.
Spurs (4-2-3-1): Lloris (c), Walker, Alderweireld, Wimmer, Rose, Dier (Chadli 90), Dembele, Lamela (Carroll 66), Alli (Mason 81), Eriksen, Kane. Substitutes (not used): Vorm, Walker-Peters, Trippier, Son.
Bournemouth (4-4-2): Boruc, Smith, Francis (c), Cook, Daniels, Surman, Arter (O’Kane 46), Ritchie, Gradel (Pugh 70), King, Afobe (Grabban 46). Substitutes (not used): Federici, Gosling, Elphick, Distin.
Goals: Spurs – Kane 1, 16, Eriksen 52.
Yellow cards: Bournemouth - Francis.
Referee: Neil Swarbrick.