Heung-Min Son scored his first Premier League goal after a quick breakaway led by substitute Christian Eriksen mid-way through the second half to settle the game in our favour.
Yohan Cabaye had hit the post prior to the interval, while Hugo Lloris pulled off a fine save to deny Bakary Sako just before the opening goal.
We defended resolutely in the closing stages to make it three wins on the spin in all competitions, with Clinton Njie also going on as a substitute for his Premier League debut.
Spurs (4-2-3-1): Lloris, Walker, Vertonghen, Alderweireld, Davies, Dier, Alli, Lamela (Carroll 87), Son (Njie 79), Chadli (Eriksen 66), Kane. Substitutes (not used): Vorm, Trippier, Fazio, Townsend.
Palace (4-2-3-1): McCarthy, Kelly, Hangeland, Delaney, Souare, McArthur (Mutch 76), Cabaye, Zaha (Campbell 46), Puncheon, Sako (Bamford 84), Bolasie. Substitutes (not used) Hennessey, Mariappa, Lee, Ledley.
Goals: Spurs – Son 68.
Yellow cards: Spurs – Lamela; Palace – Kelly, Bolasie.
Referee: Michael Oliver.