Dean Marney netted twice to give the home fans the chance to chant the name of someone other than Jermain Defoe.
Spurs were without their 15-goal top scorer who was sidelined with the knee injury he picked up against Crystal Palace in midweek, but they clearly did not miss him.
And the arrival of a strike partner for Marcus Bent cannot come too soon for Everton, as they slumped to their second straight defeat, and their fifth of the season - all of which have been against London clubs.
Spurs were first to go on the attack as early as the second minute, when Fredi Kanoute raced down the right flank to cross for Robbie Keane, who just failed to connect.
James McFadden blew Everton's first chance in the 14th minute, when he was left alone outside the box to chest down the rebound from Thomas Gravesen's corner, only to blast high over the bar.
But Marney settled the home side's nerves in the 16th minute with a well-taken goal.
The 20-year-old latched on to Keane's pass before drilling the ball high into the net.
Eight minutes after his first goal Marney had cause to shout for a penalty when Keane again put him through, only for him to tangle in the box with Alessandro Pistone.
Spurs were soon two ahead when teenage starlet Reto Ziegler got in on the act with his first goal on English soil.
The Swiss Under-21 international was perfectly placed to slot his shot in the bottom corner from Kanoute's flicked header.
Tim Cahill pulled a goal back for the visitors five minutes before the break, when he shot low and hard to beat Paul Robinson after Bent had set him up nicely with a header into the box.
Portuguese international Pedro Mendes made it 3-1 in the 59th minute, when he drilled his shot past Wright.
Marney turned provide for Keane in the 68th minute when he left Pistone for dead to cross for the Irishman, who calmly tapped in his ninth goal of the season.
Marney all but put his name on the team sheet for the rest of the season in the 80th minute when he netted the goal of the game, a 20-yarder, for Spurs' fifth.
James McFadden scored a late consolation for Everton but it took nothing away from Marney's excellent start to 2005.
MAN OF THE MATCH: Dean Marney (Spurs) - The youngster scored twice and had an exceptional game in his first start of the season.