Harry Kane fired us ahead in a thrilling game, before Toby Alderweireld nodded in Christian Eriksen's corner to make it 2-0 at the break.
Kane added our third five minutes into the second period with Kyle Walker completing our side of the scoreline on 84 minutes.
Manuel Lanzini netted a consolation for the Hammers three minutes from time, but we'd already done more than enough to claim victory.
Spurs (4-2-3-1): Lloris, Walker, Alderweireld, Vertonghen, Rose, Dier, Dembele, Son (Onomah 85), Alli (Mason 71), Eriksen, Kane (Carroll 90+1). Substitutes (not used): Vorm, Trippier, Davies, Townsend.
West Ham (4-1-4-1): Adrian, Jenkinson, Tomkins, Reid, Cresswell, Kouyate, Moses (Zarate 63), Noble (Song 80), Lanzini, Sakho, Carroll (Jelavic 63). Substitutes (not used): Spiegel, Ogbonna, Antonio, Oxford.
Goals: Spurs - Kane 23, 50, Alderweireld 34, Walker 84; West Ham - Lanzini 87.
Yellow cards: Spurs – Alli, Walker; West Ham – Noble, Sakho.
Referee: Anthony Taylor.