Everton produced a superb display of counter-attacking to climb out of the Premier League relegation zone with a stunning victory that dented Brighton’s European ambitions.

Mali midfielder Doucoure added Everton’s second just before the half-hour mark with a precise volley, into the right corner from Dwight McNeil’s cross.

McNeil was then heavily involved as Sean Dyche’s side extended their lead, driving towards the byeline and seeing his low cross deflect off the foot of Brighton goalkeeper Jason Steele into the back of the net.

A shambolic first period saw Brighton booed off at the interval, fortunate not to have suffered the embarrassment of being four goals down, with Dunk blocking James Garner’s close-range effort on the stroke of half-time.

A mightily impressive performance from Everton, who repeatedly threatened on the break during the first half and defended stoutly in the second, saw them add their fourth when McNeil raced on to Alex Iwobi’s incisive pass to round Steele and slot into an empty net.

Roberto de Zerbi’s side, who were much improved after making four half-time changes, saw substitute Evan Ferguson (twice) and Alexis Mac Allister hit the woodwork, before they finally managed a scrappy consolation with Kaoru Mitoma’s sliding effort rebounding off the post and bouncing in off Mac Allister.

A wonderful McNeil effort in added time, that flew into the top corner, ensured Everton had the final say as they moved out of the drop zone in style, to sit 17th in the table after leapfrogging Leeds United and Leicester City.

“People will be out there thinking, ‘Right, OK, there’s life in that team’ but we’ve never lost sight of that,” said Everton boss Dyche.

“It just reminds the players that their work ethic, their commitment to the cause, their commitment to the group is really important because I know there’s quality. They’re very high, feeling the feel-good factor. But it’s only another step.

“I said that after Arsenal, and sometimes people forget that. There’s three more big steps we’ve got to take.”

Everton had also briefly jumped above Nottingham Forest too but Steve Cooper’s side defeated bottom club Southampton 4-3 later on Monday.

Brighton remain seventh, seven points behind fifth-placed Liverpool, with two games in hand

Toffees find clinical edge in sensational fashion

Many Everton fans travelled down to the south coast more in hope than expectation on the back of a seven-game run without a win.

They had also been hammered 4-1 by Brighton at Goodison in January when the Toffees’ players completely fell apart. And prior to kick-off you would have had to trawl down to the eighth tier of English football to find a club with fewer league goals than Everton’s 27 this season.

However, they found their clinical edge in sensational fashion as their supporters joyously celebrated in the stands.

Calvert-Lewin’s turn away from Dunk set the tone in the build-up to the first goal, with the England forward delivering a fine display in only his fourth start in three months.

There were numerous others that excelled including Doucoure, who was out of favour before Dyche’s arrival, and scored twice for the first time in the English top flight.

Aside from his two goals, the second of which involved wonderful composure, McNeil, who covered more ground than any other visiting player (12.76km) also made telling contributions when tracking back to help out his defence.

Nathan Patterson also largely nullified the threat of Kaoru Mitoma, while James Tarkowski and goalkeeper Jordan Pickford both made important interventions to keep the hosts at bay.

Pickford notably denied Republic of Ireland forward Ferguson on three occasions, brilliantly touching a header on to the post, athletically getting his fingertips to a rasping drive that clipped the crossbar on its way to safety and then saving by his left post late on.

Everton host league leaders Manchester City next, on Sunday at 14:00 BST, which possibly makes this victory even more important.

Lacklustre Brighton pay the price

After lapping up the euphoria of their late win over Manchester United on Thursday, this marked a significant setback for a Brighton side with their sights on European football next season.

Seagulls boss De Zerbi cut a frustrated figure throughout the first half in which his normally fluent side simply imploded.

“We made a mistake in our mentality,” said the Italian. “We arrived second in every situation, especially in the first half. It was too easy. We made too many mistakes. If we want to achieve our target, we can’t make these mistakes.”

Dunk was clumsily caught the wrong side of Calvert-Lewin for the opening goal and his central defensive partner Adam Webster was at fault for the second – losing the ball high in the Everton half.

Steele’s poor positioning cost them a third goal as the ball flicked off his heel and even Everton’s fourth saw McNeil afforded the freedom of the Amex Stadium, to dance past the goalkeeper and raise his arms aloft before prodding the ball over the line.