Timing is everything, and at the end of a week that brought hope of a new era for Everton under the Friedkin Group, Sean Dyche finally tasted a first Premier League win of the season. A fresh start does not have to be confined to the boardroom.

Everton claimed their first three points courtesy of a superb double from Dwight McNeil plus a second-half transformation. By both teams. Defeat was galling for Crystal Palace. Oliver Glasner’s team controlled the first half and deservedly led through Marc Guéhi’s poacher’s finish. But for a careless final ball their lead could have been greater.

Related: Tomas Soucek salvages point for West Ham after Brentford strike early again

However, as Glasner correctly put it: “We lost the game in 15 minutes.” McNeil caught Palace cold with a stunning equaliser two minutes after the restart and they did not recover. Everton, better organised, harder working and more resilient, produced the first comeback victory of Dyche’s reign. For the first time this season, they also managed a lead securely.

“We tried to correct a few things,” said Dyche of his half-time team talk. “But mainly it was about telling them that everyone has to make a difference and not wait for someone else to do it. It was a nervy stadium to get our first win but we handled the second half very well and they were two great moments from Dwight.”

The Palace trio of Adam Wharton, Daichi Kamada and Eberechi Eze ran the show in the first half, dissecting Everton’s midfield repeatedly. Dyche’s response, dropping Orel Mangala deeper to contain Eze, contributed significantly to the hosts’ recovery.

A first appearance of the season for Jarrad Branthwaite gave Everton hope of much-needed defensive improvement but they shipped another set-piece goal. The ineffective Jesper Lindstrøm appeared to have dealt with Wharton’s corner only for Kamada to dispossess the winger inside the penalty area. Wharton’s second bite was floated to the back post, where Daniel Muñoz headed down for Guéhi to convert at the near post. James Tarkowski and particularly Jordan Pickford were unconvincing in reacting to the danger.

Pickford had a few first-half lapses, spilling a Jefferson Lerma header from another Wharton corner. Iliman Ndiaye saved the Everton goalkeeper by blocking Muñoz’s follow-up. Tarkowski blocked Eddie Nketiah’s drive from the resulting corner, sending the ball spinning towards his own goal. Pickford was unable to collect and this time Ashley Young intervened with a vital clearance. Tarkowski took both ball and man when Jean-Philippe Mateta cut inside Branthwaite inside the Everton area. The referee, Andrew Madley, allowed play to continue until the central defender scythed through Eze too.

Boos followed Everton down the tunnel at half-time. They were transformed by the collective effort to shut down Palace’s midfield dominance and two flashes of individual brilliance from McNeil. Young, who enjoyed a fine game, intercepted Kamada’s pass towards Eze. The veteran found McNeil in space and, from 25 yards out in his new central position, the No 7 curled a magnificent shot beyond Dean Henderson. It was similar to a match-winning goal that McNeil fired into the same net for Dyche’s Burnley three years ago. He was not done there.

Lindstrøm’s half-time replacement, Jack Harrison, created McNeil’s second with a delightful cross to the far post after Palace failed to deal with Pickford’s free-kick. McNeil flicked the ball up and over Nketiah, then swept home an unstoppable volley under Henderson.

• Download the Guardian app from the iOS App Store on iPhone or the Google Play store on Android by searching for 'The Guardian'.

• If you already have the Guardian app, make sure you’re on the most recent version.

• In the Guardian app, tap the Menu button at the bottom right, then go to Settings (the gear icon), then Notifications.

• Turn on sport notifications.

The game, mood and belief had turned on its head. Abdoulaye Doucouré should have sealed victory when played through by Dominic Calvert-Lewin but delayed long enough for Maxence Lacroix to intervene. Palace piled on the pressure in the closing stages with Goodison gripped by tension having seen Everton squander three successive leads in the league. But not this time. Branthwaite, Tarkowski and Young were to the fore as they repelled the visitors’ loaded frontline.

“For many parts of the game it did not look like we would lose,” Glasner lamented. “But we were not ready for the second-phase situation twice and we gave them momentum. Now we need to stick together and roll our sleeves up.”