David Moyes has not only created a new-manager bounce at Everton, he has engineered a gravity-defying leap when compared to what preceded him at Goodison Park. Famine to feast is putting it mildly.

Sean Dyche needed five months and 19 games to win three Premier League games this season. Moyes has matched that in 14 days and four matches.

Before Beto’s double, the last player to score twice in a Goodison fixture for Everton was Craig Dawson. That was into his own net as a Wolves defender.

Everton could barely create a chance three weeks ago, years of attritional football presented as symptomatic of a broader, institutional malaise. Dyche’s side managed just seven goals from open play this season. Everton now have six from open play in the last two home games.

It is rather like Moyes has returned to Merseyside with an industrial-powered vacuum to suck out all of the contaminated air, the poisonous negativity replaced by the sense Everton may soon be back where they were during the Scot’s first Goodison era.

That was a time when it was often said: “If he can make them look this effective at Goodison with limited resources, what will he do with a bit more cash?”

Moyes says he is a different manager at a different Everton. It’s true. Older and wiser, what is immediately striking is Moyes’ sense of relaxed authority. He has unrivalled knowledge of what makes this club tick, and that sense of trust is filtering from the stands into the players as – for the first time in many years – the Goodison crowd do not just believe, they know they are in safe hands.

“We wanted to find a few more goals. The players have just given themselves confidence and positivity,” Moyes said, deflecting credit to his squad while thinking of the next steps. “We are trying to give ourselves more time on the ball. I want to add composure. We are beginning to play better. But going forward, the level of players we are going to need will dictate how we go.”

For now, Everton are grateful to be reaping the rewards from a manager in a hurry to escape peril. Moyes expressed his determination to avoid being branded a specialist coach summoned to save teams from relegation. He could not have anticipated the speed with which Everton have dragged themselves away from the bottom three. Nothing will be taken for granted yet – he reiterated the need for reinforcement before the transfer window closes – but they already look in a different league to Leicester City. On this evidence, they will be soon enough.

They could not have been sharper out of the blocks, Abdoulaye Doucouré scoring Goodison Park and Everton’s quickest-ever goal after 10 seconds. It was the fourth fastest to be registered in Premier League history.

“After 10 seconds I was thinking: ‘This is fabulous,’” said Moyes.

The ease with which Doucouré found space and time from Jordan Pickford’s long ball signposted how dire Leicester’s defence would be. Any renewed optimism after beating Tottenham Hotspur last weekend was snuffed out within six minutes when James Tarkowski picked out Beto for a near-identical finish as Doucouré’s.

As the visiting fans chanted their disapproval with the board – the customary default position whenever players and coaches serve up such dross – it momentarily felt like their manager, Ruud van Nistelrooy, would do well to survive in post beyond half-time.

“We are better than we showed today. That is clear,” said the Dutchman. “The focus is on this squad. You saw last week what they were capable of. It is about getting the best out of them again consistently.”

Leicester’s misery was compounded when Beto cleverly struck Everton’s third before the interval, and excellent Iliman Ndiaye added a fourth on 90 minutes after more hapless defending.

Leicester should plan ahead for next season’s promotion push. They never won a tackle or second ball, and their first shot on target was after 73 minutes. They might as well have stuck with Steve Cooper.

While Moyes may soon have the luxury of looking ahead to next season in a new arena and a desire to reach for the skies, Van Nistelrooy, in grim contrast, is overseeing a new-manager plunge.