This was probably the day when West Ham’s unlikely dream of qualifying for the Champions League fell apart. Although their challenge is not over yet, the sight of Vladimir Coufal slumping to the ground in despair at the end told a story. The right-back had come closer than anyone to rescuing a draw for West Ham and it probably did not help the Czech’s mood when he saw Dominic Calvert-Lewin lying on his back a few yards away, taking a few moments to recover from his tireless performance in Everton’s attack. The margins were fine. Whereas Coufal’s angled shot hit the inside of a post and bounced into Jordan Pickford’s grateful arms in the 61st minute, Calvert-Lewin was ruthless when his moment arrived. The Everton striker’s clinical finish summed up the difference between the sides. The pressure was too much for West Ham and although it was impossible to fault them for effort, they could not match Everton’s greater conviction in the final third. Everton, who are up to seventh and have a game in hand on West Ham, deserved a win that keeps their hopes of European football alive. Carlo Ancelotti’s side were measured in midfield, defiant at the back and sharper up front, earning the points thanks to Calvert-Lewin’s 21st goal of the season. “We managed the game well,” Ancelotti said. “It was important to feel how important this game was. The motivation was really high.” This was a bad moment for West Ham, who are five points below Leicester with three games left, to misplace their composure. Too many of David Moyes’s forwards were off their game. Jesse Lingard’s ruthless touch eluded him for once. Michail Antonio battled without reward. Clear chances were rare and Saïd Benrahma was wasteful when one arrived, heading over when he could have gone a long way towards justifying West Ham’s £30m outlay on him last summer. Benrahma, yet to score since joining from Brentford, had a poor game on the left flank. Nothing quite clicked for West Ham in the final third and they lacked their usual intensity in midfield, struggling as Everton pressed high to force errors. The problem for West Ham was partly that Manuel Lanzini was too lightweight a partner for Tomas Soucek, who is not the same force without Declan Rice alongside him in midfield. Rice was still not ready to return from his knee injury and with Mark Noble also missing, Everton were able to impose themselves in the first half. Everton had the tactical edge thanks to Ancelotti’s 3-5-2 system. Tom Davies and Allan offered bite in midfield, snuffing out West Ham’s creative talents, and provided the visitors with a platform to push forward. Gylfi Sigurdsson was lively and Richarlison threatened up front, repeatedly spinning away from Issa Diop. It came as no surprise when Everton scored in the 24th minute. West Ham gave Ben Godfrey time to step into midfield and the centre-back punished them by releasing Calvert-Lewin, who had the pace to evade Craig Dawson and the composure to drill a low finish beyond Lukasz Fabianski. “The goal of a top striker,” Ancelotti said. Moyes was less generous than Everton’s manager, calling it “a terrible goal” and criticising his side’s defending. Yet it was no more than the visitors deserved and they could have extended their lead before the break. Fabianski pushed Sigurdsson’s free-kick over and saved well from Richarlison. West Ham, did not have a shot on target, although they should have equalised when Pablo Fornals crossed from the right. Benrahma was unmarked and lost his nerve when it looked easier to score. At least it was a reminder of West Ham’s threat. Everton fell back in the second half and had to defend well. They needed Michael Keane, Yerry Mina and Godfrey to stand up to Antonio. They also needed a slice of luck when Fornals found Coufal, arriving from right-back and desperately unlucky to see his shot hit the far post. Jarrod Bowen, who came on for the injured Lanzini, could not latch on to the rebound. While they huffed and puffed, West Ham did not create another chance. Everton got their blocks in and their defence headed everything away, even though Mina had to make way for Mason Holgate. They even could have added another on the break, only for Joshua King to head against the left post after replacing Richarlison. When it was over Calvert-Lewin fell to the turf out of sheer exhaustion. The striker had given everything to the cause. It was West Ham who had run out of steam.