Richarlison opened the scoring against his former club with his fourth goal in three matches, before Son Heung-min doubled Spurs' advantage soon after.
Everton deservedly pulled a goal back through Andre Gomes, in his first Premier League game since May 2022.
But Spurs move above Manchester City - absent from league action due to the Club World Cup - into fourth.
Defeat for Everton ended a four-match winning run and leaves them just four points above the relegation zone.
Brazilian Richarlison put the hosts ahead after just nine minutes, slotting in Brennan Johnson's low cross at the near post.
Son doubled Spurs' advantage soon after, with Johnson again providing a key supporting role. The Wales international picked the ball up from a short corner and fired in a powerful drive which Everton keeper Jordan Pickford palmed away.
It fell to Son, who slid the ball home with Pickford caught in a crowd of players and unable to intervene.
Everton showed plenty of attacking intent in an entertaining match and Dominic Calvert-Lewin scored five minutes after half-time - only for the video assistant referee to disallow the goal following a foul by Gomes on Emerson Royal in the build-up.
Gomes, who spent last season on loan at Lille before suffering a calf injury, made some amends with a fine volleyed strike on 82 minutes to set up a grandstand finish, but Spurs held on.
-- Courtesy of BBC Sport