The visitors could have taken the lead in the opening minutes, but Louis Saha's shot flashed inches wide of the post.
Emmanuel Aderbayor fired over from a tight angle for the hosts before the on-loan striker could have done better when the ball was squared to him by Gareth Bale.
Spurs soon began to take control of the match as Adebayor saw another effort fly wide, while Rafael van der Vaart's curled drive breezed over.
Aaron Lennon finally gave Spurs the lead just before the half-hour when he cut inside before driving his shot past Tim Howard.
Harry Redknapp's side doubled their lead early in the second half through Benoit Assou-Ekotto's long-range deflected drive.
Leighton Baines's tackle was enough to stop Adebayor adding a third for Spurs, while Van Der Vaart saw another shot go over.
Everton could have had a penalty in the final ten minutes when substitute Royston Drenthe looked to have been felled by Younes Kaboul. However, referee Martin Atkinson waved away the appeals.