It turns out David Moyes replacing Sean Dyche was nothing like copy and paste. One British manager is not the same as the next. Each of the players decisive in victory at Crystal Palace exemplified the influence and nous Moyes has returned to Merseyside.

Beto, a striker untrusted by Dyche, scored a fine goal. The late winner came from an astute wild-card signing in Carlos Alcaraz, the supplier of Beto’s earlier goal smashing in the rebound of a shot from Ashley Young, a player Moyes worked with back in their Manchester United days.

Related: Crystal Palace v Everton: Premier League – live

If there was nothing like the fervour of the midweek Merseyside derby, Everton exerted an ability to tough out matches, a quality that previously felt lost for ever. Their defence, recovering their shape after previous wobbles, ended the match heading away everything Palace threw at them. Victory made it 13 points from six matches since Moyes’s return. Everton are mid-table, above Manchester United, Tottenham and West Ham.

“It has been a brilliant start, it was a good win for us, really scrappy,” said Moyes. “They showed great resilience. There’s a much better togetherness with the supporters and the players.”

Wednesday’s derby efforts had increased Moyes’s casualty list to nine first-team absentees. Iliman Ndiaye, consistently Everton’s best player, has a medial knee ligament problem. Abdoulaye Doucouré’s high spirits in the Goodison aftermath had landed him a ban.

Oliver Glasner and Moyes are old adversaries, the Austrian’s Eintracht Frankfurt beating Moyes’s West Ham on the way to winning the Europa League in 2022. Having beaten West Ham last season, Glasner’s quest for four successive wins over Moyes was denied. “It is not a game we should lose,” said the beaten manager. “We didn’t have the efficiency today.”

Everton began as if unable to shake off residual lactic acid. “Wednesday took so much out of us,” said Moyes. In the opening seconds, Jarrad Branthwaite slashed at fresh air, Wednesday’s last-minute hero James Tarkowski slipped and Jordan Pickford’s low save from Jean-Philippe Mateta rescued blushes.

The ever vocal Pickford soon had to save Marc Guéhi’s header. From the resultant corner, Jefferson Lerma’s header flew in, only for the linesman and the video assistant referee to rule that Justin Devenny’s kick had swung out of play and back in. The ever-clunky stadium technology first declared “Goal” then hurriedly corrected itself to “No goal”. Work to do on that user experience. Palace’s finishing, too. A goalmouth scramble presented the ball for Ismaïla Sarr to slap off the crossbar.

Within seconds, Tyrick Mitchell’s poor throw offered Alcaraz some space. His pass was poked to Beto, whose finish showed a coolness unseen during Dyche’s tenure. “I am playing with more confidence and joy,” the striker said.

Alcaraz, once of Southampton, on loan from Flamengo, goes against the accusation that Moyes distrusts mavericks; he will, as long as other, less glamorous work is put in. Moyes said of his scorers: “Beto’s chances have come through injury, he probably saw a chance to play half a dozen games or so. It was down to him to show if he was capable … Carlos has done a great job for the team.”

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Glasner’s half-time response was to bring on Adam Wharton and Eberechi Eze. Last season’s leading lights are struggling with injury. “They are not in the best shape,” said Glasner, though within seconds of play resuming, Mateta had lashed in Guéhi’s overhead flick of a second-ball rebound. VAR dithering led to almost four minutes of delay. The players warming up in the cold, as Anthony Taylor waited for confirmation, added a Busby Berkeley-style formation-dance to farcical proceedings.

“We had momentum,” said Glasner, but Everton retained danger on the counter. Jesper Lindstrøm set up Beto for a pair of attempts that Palace goalkeeper Dean Henderson eventually scrambled away. On came Ben Chilwell for a first Selhurst home appearance, Glasner exerting a greater depth of resources over Moyes, who said: “We are so short of players.” Overlapping from left-wing back, the Chelsea loanee scooped a shot that Pickford deflected behind.

Moyes then brought on his own former England left-back in Young, 40 in July, to play his part in a win that extended the question of why manager and club ever allowed themselves to be parted.