Spurs manager Jose Mourinho included new signings Matt Doherty and Emile Hojbjerg in the line-up while his opposite number Carlo Ancelotti also named James Rodriguez, Abdoulaye Doucoure and Allan in his line-up.
Richarlison had a big chance to give Everton the lead in the 15th minute after racing clear on goal from the blind side and got past goalkeeper Hugo Lloris at the near post but with the net opening up and an option of a cut-back, he blasted his strike high and wide.
Jose Mourinho’s charges came very close to breaking the deadlock just after the half-hour mark from a counter-attack, as Dele Alli got a pocket of space from a late run inside the box but his looping shot was parried over the bar by shot-stopper Jordan Pickford.
Doherty was unlucky not to score on debut for the hosts just before the break after a dink over the defence by Harry Kane sent him clear on goal at the near post but his side-footed shot searching for the bottom corner was saved by Pickford with his foot as the first stanza ended goalless.
Ancelotti’s troops eventually broke the deadlock ten minutes from the break after Dominic Calvert-Lewin powered home a header into the top corner after a pin-point cross by Lucas Digne.
Richarlison had a good chance to double Everton’s lead in the last 18 minutes after cutting inside from the left wing but his curling shot missed the far post by a whisker.
The game was on the edge in the closing stages, with the visitors threatening on counter-attacks while Spurs were putting on the pressure but unable to find the decisive pass in the last third.
In the end, the Toffees managed to hold on to snatch all the three points and move up to sixth on the log while Spurs were left without points.