Goals from Joleon Lescott, Leon Osman and Alan Stubbs ensured David Moyes' side made it six points from their opening two games and showed they are going to be a real force again this season.
Tottenham, who were many people's favourites to break into the top four this season, have now lost their opening two games and the pressure is already mounting on manager Martin Jol, who has spent nearly £40million during the summer.
Following their opening day defeat against Sunderland, the Spurs boss took drastic action and handed a full debut to summer signing Darren Bent who was picked to play alongside Dimitar Berbatov and Robbie Keane.
But the move backfired as Everton stunned the home support when they opened the scoring after just three minutes.
Mikel Arteta's free-kick picked out Lescott who rose above Anthony Gardner and flashed a powerful header past Paul Robinson.
Bent almost got off to a dream start on six minutes when he had the ball in the back of the net but his effort was ruled out for offside against his striker partner Berbatov following a neat interchange.
Bent was involved in the heart of the action once again on nine minutes.
Pascal Chimbonda's ball picked out the England striker who fired a low right-foot shot which produced a fine save from Tim Howard diving low to his right.
Everton striker Andy Johnson - who is competing with Bent for a place in the England side against Germany next week - then showed his qualities on 14 minutes.
Johnson forced his way past Chimbonda down the left and cut the ball back for Victor Anichebe whose low shot produced a fine save from Robinson.
The home side suffered a major injury blow on 18 minutes when Younes Kaboul was forced to leave the field through injury and was replaced by Ricardo Rocha.
But Tottenham kept battling away and almost drew level on 23 minutes after Keane produced a sublime piece of skill to lift the ball over two Everton defenders.
The ball fell to Berbatov, but the Bulgarian international fired his close-range shot over the bar.
Tottenham got their just rewards when they snatched an equaliser on 26 minutes.
Gardner managed to get his revenge on Lescott when he lost him in the penalty box and directed his header past Howard.
But Everton quickly showed their fighting qualities when they regained the lead on 37 minutes.
Rocha could only clear Arteta's chip straight into the path of Osman who was unmarked in the box and made no mistake smashing the ball into the roof of the net.
Things were to get even worse for the home side when Everton added a third on the stroke of half-time.
Stubbs hit a fierce free-kick which deflected off Didier Zokora and flew past Robinson into the corner.
Berbatov should have pulled a goal back for Tottenham on 48 minutes but his header cannon back off the post.
Substitute Jermain Defoe was then denied on 78 minutes after his half-volley produced a superb reflex save from Howard in the Everton goal.
The defeat leaves Tottenham rooted to the foot of the Premier League table after two fruitless matches.