The Toffees have picked up form since Moyes replaced Sean Dyche, and made it three league wins in a row for the first time this season in style.

Doucoure gave them lift off after just 10 seconds, latching onto Jordan Pickford's long ball to drill home his speedy strike.

Beto doubled Everton’s tally soon after with an assured finish after being put through one-on-one and then made it 3-0 in first-half stoppage-time in similar fashion, capitalising on unconvincing Leicester defending and exposing its high defensive line after a fine pass from James Garner.

Jesper Lindstrom should have made it 4-0 midway through the second half, but sent a tame finish straight at Mads Hermansen.

Iliman Ndiaye made no such mistake as he capitalised on a defensive mix-up to add further gloss late on as Everton continued its charge away from the relegation battle.

Everton manager David Moyes reserved special praise for Bet after the game, highlighting his importance to the side with the likes of Calvert-Lewin and Armando Broja on the sidelines for a lengthy period of time.

"I'm really pleased for Beto because I'm only just getting to know him. He's probably felt it's been difficult for him," Moyes said.

"We need someone to score goals – we're short on centre forwards and losing Dom was a big blow – he came in and took his goals very well."

Moyes was delighted with his side's first-half showing, noting the importance of Doucoure's fast opener. 

"When you get a goal so quickly it's a great confidence boost," Moyes said.

"We backed it up with the second goal, which allows us to play. We were a bit unlucky to score a few more at that time. At times, our first-half performance was very good."

The Goodison faithful was singing Moyes's name towards the end of the match and the Scotsman is aware of what he still needs to see from his side to ensure it remains a Premier League side and make the last remaining matches at Goodison Park difficult for away teams.

He said: "I found the noise incredible.

"I remember what it was always like. You have to give them something to shout about, and we did that from the start.

"We're doing a lot of good things. There's a lot we can try to make better. The job is to make sure we're a Premier League team. The last three results will go a long way to making that happen."

Leicester boss Ruud van Nistelrooy admitted that a calamitous start proved too much to overcome for his players, with his side going two goals down after just six minutes.

It ended a run of seven straight defeats in the competition by beating Tottenham Hotspur last time out, but could not build on that result here.

"If you look at the scoreboard after 10 seconds and after five minutes if you look at the goals, of course, you don't do yourself any favours to come here and get a result starting like that," he said.

The Dutchman was also disappointed with the defending by his side for the opening two goals.

Leicester lost the first aerial duel of the encounter, leading to Doucoure bursting into the box and putting the home side in front, while a simple weighted pass by James Tarkowski put Beto clean through for the second.

He added: "You look at the first long ball, a duel, Doucoure is in. The second one, one ball down the channel. Good finishes. They were very effective.

"We know the start of the game you have to stay in the game. You know it will be intense and hard at Goodison. We gave ourselves a big problem to get a result.

"It's little things. The first duel and sharpness to act accordingly. It can happen, it's football. We know the situation we’re in. We're together and want to push forward and get out of the situation."