Amid news of a new takeover attempt at Everton during the week, the hosts also provided renewed hope on the pitch, as they continued their fine form against Palace at Goodison Park.

Marc Guehi gave the visitors an early lead, poking home at the near post, seeming to signal the continuation of Everton’s woes.

But Dyche’s side rallied after the break, with McNeil hitting the back of the net with a delightful long-range strike in the 47th minute before adding a second at the far post just seven minutes later.

Abdoulaye Doucoure had the opportunity to put the game to bed 10 minutes from the end as Dominic Calvert-Lewin set him through on goal, but a last-ditch challenge from Lacroix spared Palace’s blushes.

The win lifts Everton out of the relegation zone and into 16th, leapfrogging its opponent, which drops to 17th and still doesn't have a win of its own.

Dyche expressed his relief after the game.

"You know there’s been question marks over many things, and of course, there's been a bit of relief there for me today and relief for the players, and that’s a human thing," he said.

"There's a lot of demand here that we put on ourselves and we have to answer to that and I thought we did today. We certainly did enough to win the game and that’s what was important."

"When you haven’t got that first win you feel nervous. Then you go 1-0 down, the stadium becomes awkward for the players.

"I spoke to them in the second half about being someone who makes a difference. It’s every person that counts, not just one."

Crystal Palace had the better share of possession with 59.4 per cent, a source of disappointment for boss Oliver Glasner.

"Over 70-75 minutes we controlled the game, but you must be focused all game. It is a big strength of Everton's in set-plays. They do it well and we defended it most of the time really well," he said.

"We tried everything, we changed the system, brought on all our offensive players. They defended with 10 players around their box so we didn't have a lot of space so it was difficult.

"Today we couldn't score the equaliser. If you concede two goals it's not so easy to get a point or to win."

It leaves the visitors without a win in their past six games in the Premier League. 

"We know it when we look at the table," Glasner added.

"Maybe it is a welcome back to reality. Maybe we were flying too high after a great finish to the season. The Premier League is a fight."