And despite a good start, the Terriers were behind on nine minutes, as Harry Kane raced away to score with a low shot.
And it was 2-0 to the visitors on 17 minutes, Ben Davies firing home.
Huddersfield: Lossl, Smith, Jorgensen, Schindler, Lowe, Mooy, Hogg, Kachunga, van La Parra, Ince, Depoitre. Subs: Malone, Whitehead, Billing, Sabiri, Cranie, Green, Hadergjonaj.
Tottenham Hotspur: Lloris, Alderweireld, Sanchez, Vertonghen, Trippier, Winks, Dier, Davies, Eriksen, Alli, Kane. Subs: Son, Vorm, Nkoudou, Sissoko, Llorente, Foyth, Walker-Peters.
Referee: Neil Swarbrick (Lancashire)