Son Heung-min scored an open goal for Tottenham after a nightmare mistake from Everton goalkeeper Jordan Pickford.
Sean Dyche's side went into the clash at the Tottenham Hotspur Stadium wanting to avenge last weekend's 3-0 home defeat to Brighton, which saw them finish with 10 players.
But it was hardly the greatest start, with Yves Bissouma - returning to the Spurs team after his club-enforced one-match suspension - putting the hosts in front inside 14 minutes.
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It was then 2-0 on 25 minutes through Son's first goal of the season - but it was scored in the worst possible circumstances for the Toffees.
A throw-in from young debutant Roman Dixon went backwards to Michael Keane, who elected to pass it back to Pickford.
The England goalkeeper took a heavy touch, but was closed down by Son, who won the ball from him and tapped it into the empty net.
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It has hardly been a convincing start to the season for the Toffees, who are lacking depth in key areas and are yet to score a goal in 135 minutes of action.
Dyche has also received some criticism over his team selection, with Keane preferred to new signing Jake O'Brien despite his indifferent form last season.
Spurs, meanwhile, drew 1-1 with Leicester on the opening weekend of the season - with manager Ange Postecoglou demanding that his team show a reaction after full-time.
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He told Sky Sports: "First half, excellent, controlled the game. Wasteful in front of goal.
"The second half was the same. We started off well, wasteful in front of goal. Once Leicester scored, you could tell they lifted, the crowd lifted. We lost our composure and let them back in the game.
"I don't buy ring rust. It's an issue we had last year as well - we need to keep working hard at it and being more ruthless in front of goal."
Topics: Jordan Pickford, Son Heung Min, Everton, Tottenham Hotspur, Premier League, Football
Ryan Smart