As Jordan Pickford basked in his first penalty save since the World Cup, Roy Hodgson visibly sunk in despair. He knew. His Crystal Palace team had been strong, they had been dangerous, but they were ultimately punchless and pointless. It is becoming the recurring theme of their season. Everton timed the execution to perfection.

Two goals in the final three minutes from the substitutes Dominic Calvert‑Lewin and Cenk Tosun, the former’s crucial breakthrough created by another substitute, Ademola Lookman, brought Marco Silva his first hat-trick of Premier League wins as Everton manager and a familiar lament from his opposite number.

Everton 2-0 Crystal Palace: Premier League – as it happened Read more

Only Huddersfield Town have scored fewer goals than Palace this term and profligacy cost the visitors yet again at Goodison Park. Luka Milivojevic failed to beat England’s No 1 from the penalty spot with the contest delicately poised and, despite the vibrancy offered by Wilfried Zaha and Andros Townsend at the head of Palace’s attack, the absence of a genuine marksman was glaring when Hodgson’s team were ascendant. Pickford’s penalty save, Everton’s resolve and Silva’s substitutions combined to turn the game.

“We came across a goalkeeper in form who made two outstanding saves in the first half as well as from the penalty,” the Palace manager said. “Then they scored in the 87th minute to aggravate things and then a second from a long clearance that made the scoreline even harder to take. The penalty would have made a difference. Instead it lifted the crowd, they really got behind their team, and it gave them fresh impetus going forward. They were able to risk a bit more but I still think it was harsh. I am sure people would not have begrudged us a result.”

By contrast, this was a hugely satisfying win for Silva, maintaining Everton’s recent momentum and demonstrating the improving depth of his resources with all three substitutes making a telling impact. There was a fresh, balanced look to the Everton team with André Gomes making his first appearance since a summer loan from Barcelona, and impressing, but until the final exchanges they found Palace obstinate and awkward opponents. Like others, however, they benefited from Palace’s limitations in front of goal.

James Tomkins was first to send Hodgson apoplectic in his technical area when steering a free header wastefully wide from Townsend’s inviting delivery. Minutes later his team were denied by a combination of Pickford and the crossbar. The Everton keeper foiled Milivojevic for the first time in the game from a 25-yard free-kick. From the resulting corner, Tomkins was unmarked at the back post and headed across goal for Cheikhou Kouyaté to head against the woodwork from close range. Kouyaté then headed a clearer opening wide.

Facebook Twitter Pinterest Everton’s Jordan Pickford celebrates after saving a penalty kick from Crystal Palace Luka Milivojevic (bottom). Photograph: Jan Kruger/Getty Images

Palace were physically strong, compact and disciplined – a recipe to frustrate – and should have opened the scoring when awarded a penalty on the hour. Zaha won it, much to the consternation of the home crowd who were incensed when he escaped a booking for diving seconds earlier. They could have no complaints on this occasion. Turning back inside the fit-again Séamus Coleman, Zaha was caught on the ankle by the Everton captain and referee Anthony Taylor was well-placed to spot the offence.

Milivojevic struck the penalty hard and low but straight down the middle of Pickford’s goal. The keeper intervened with his feet, sending the ball skyward and Goodison into uproar. It was Pickford’s first penalty save since the shootout against Colombia and a turning point in Everton’s afternoon.

Lookman and Calvert-Lewin had only been on the pitch for five minutes, replacing Theo Walcott and Gomes respectively, when one fed the other for a late breakthrough. Found in space on the left by Richarlison, Lookman floated a delightful ball into the six-yard box where England under-21 international Calvert-Lewin was perfectly placed and unmarked to head beyond Wayne Hennessey.

Two minutes later, Palace were caught out when pushing for an equaliser. Jeffrey Schlupp was harried out of possession by Gylfi Sigurdsson and when Michael Keane launched a clearance upfield it sent Tosun racing clear of Mamadou Sakho. The Turkey international strode through confidently and applied a finish to match, beating Hennessey with a powerful low finish.

“Sometimes you change and everything goes well, like this afternoon, and other times it doesn’t work the same,” the Everton manager said. “But the important thing is that we tried. We changed the formation when we brought on Dominic and they all did well. It is important when three players come on and they change the game. It is not just about 11 players. It is hard for me to do the squad list at the moment and that is good for the squad and for the club.”