The Toffees dominated proceedings against a sluggish Tottenham side and Calvert-Lewin opened his account for the season with an unerring header in the 55th minute.
They could’ve won more convincingly with Richarlison missing a series of chances but it was the ideal start to Carlo Ancelotti‘s first full season.
Jose Mourinho lost on the opening day of a Premier League season for the first time in his managerial career.
Everton monopolised possession in the opening exchanges with Allan orchestrating play from a deep-lying midfield role. The visitors had the first opening when a disastrous cross-field ball from Ben Davies presented Richarlison with a golden chance. Toby Alderweireld lost a foot race with the onrushing Brazilian forward and Richarlison charged past Hugo Lloris but failed to hit the target.
After virtually being spectators during the early stages, Tottenham began to counter-punch Everton by threatening on the counter-attack. Son Heung-Min tested Seamus Coleman by looking to break in behind him utilising his supreme pace and tricky feet.
Matt Doherty advanced very high which required Ben Davies to play deeper and narrower to facilitate his attacking runs. Son tricked his way past Coleman on the left and delivered a teasing cross which narrowly eluded the outstretched right leg of Harry Kane.
Spurs looked to unlock the Everton defence on the counter-attack and Dele Alli drew an impressive save from Jordan Pickford just past the half-hour mark. Tottenham raced away on a dangerous counter-attack, which was initiated by Lucas Moura, who swept the ball forward to Son. Kane tore through the middle with a determined run but Son opted to find Alli. His powerful strike was diverted over the crossbar by Pickford – leaving Kane aggrieved at Son for not slotting the ball into him.
James Rodriguez enjoyed an impressive first 45 minutes for the Toffees and cut inside onto his left foot to curl a delicious low strike from range marginally wide of the far post.
The Colombian international frequently drifted inside from his original position on the right wing. He was very progressive with his passing and was always looking to use his imagination to unlock the Spurs defence.
Tottenham started to click into gear on the cusp of half-time and Pickford was forced into a crucial save to thwart Matt Doherty. The former Wolves full-back linked effectively with Kane, who applied a deft chip over Michael Keane to present Doherty with a good chance. Pickford was alert to the danger and emerged from his goal to foil him at his feet and rescue Everton from trailing at the break.
The second half started in a similar pattern with Everton dominating possession and posing a threat via the creativity of Andres Gomes and Rodriguez. Everton drew first blood when Calvert-Lewin sprung into a devastating leap to tower above Eric Dier and head Lucas Digne’s free-kick into the top corner in the 55th minute.
Richarlison began to exploit debutant Doherty and came close twice from range. Both Doherty and Pierre-Emile Hojbjerg failed to make an impression and Mourinho withdrew Doherty with 76 minutes on the clock.
Spurs responded poorly to going behind and looked lethargic and static out of possession. They lacked intensity and desire and simply allowed Everton to control the ball rather than attacking them and looking to change the tide in their direction.
Tottenham Hotspur: H Lloris; M Doherty (T Ndombele 76′), T Alderweireld, E Dier, B Davies; P Hojbjerg, H Winks (S Bergwijn 60′); Lucas Moura, D Alli (Sissoko 46′), Son; H Kane.
Subs not used: J Hart, S Aurier, D Sanchez, E Lamela.
Everton: J Pickford; S Coleman, M Keane, Y Mina, L Digne; A Doucoure, Allan; Richarlison, A Gomes (G Sigurdsson 68′), J Rodriguez (T Davies 90′); D Calvert-Lewin (M Kean 89′).
Subs: J Virginia, J Kenny, T Walcott, Bernard.