Wild celebrations in one small corner of an otherwise deserted Goodison Park encapsulated a momentous, historic day for Luton. For the first time since April 1992, when Brian Stein and Mark Pembridge scored in a 2-0 win over Aston Villa, they had a top-flight victory to savour after inflicting fresh torment on clueless Everton. And relish it they did.

“It is an amazing day for the supporters, they deserve it and the board deserve it too,” said Rob Edwards, the Luton manager after goals from Tom Lockyer and Carlton Morris, both from Alfie Doughty set-pieces, produced the club’s first win in the Premier League.

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“They’ve really stuck with us and I know they will because we’ve been on a brilliant journey, but it’s important we give them something to shout about as well. I know it’s a big moment, and I don’t want this to sound arrogant, but I really fancied us today. I really believed we could cause them problems and win the game.”

Edwards’s justified confidence was a damning indictment of Everton’s home form and Sean Dyche’s tactics. His club picked an awful moment to lose a fourth consecutive home league game from the start of the season for the first time since 1958-59. Everton’s prospective new owners, 777 Partners, were in attendance in the form of co-founders Josh Wander and Steven Pasko plus the CEO, Don Dransfield. They have been doing the rounds this past week trying to reassure fans and politicians over their future intentions for Everton. That is a hard task given another of 777’s clubs, Vasco da Gama, were hit with a Fifa transfer ban on Friday over late payments on three transfer deals.

Two encouraging away wins in five days suggested Everton had turned a corner. But they immediately reverted to type on home soil, missing several chances and compounding their problems at one end of the pitch with poor defending at the other. Dyche’s description of a dominant display with countless opportunities going astray, however, was a gross exaggeration. His team ran out of ideas quickly and rarely threatened Thomas Kaminski’s goal in the second half, even after Luton lost the defenders Lockyer and Reece Burke to injury.

Everton were given several warnings about Doughty’s set-pieces before falling behind when Morris headed his corner against the crossbar. Ashley Young took too long to clear the rebound and Lockyer, alert to the opportunity, launched himself in front of the veteran’s clearance to divert home.

Luton were in dreamland when doubling their lead moments later. A Doughty free-kick caused the damage this time, along with Everton leaving a big, lone centre-forward with a number nine on his back unmarked at the back post. Morris, having peeled away from Vitaliy Mykolenko unnoticed, steered a superb finish into the far corner.

Dominic Calvert-Lewin spared Everton the embarrassment of becoming the first team in top-flight history to lose their opening four home games without scoring by scrambling in his third goal in three matches. A lengthy VAR check for offside against Amadou Onana and Calvert-Lewin found in Everton’s favour and the floundering hosts had a lifeline. They lacked the composure and quality to capitalise.

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Dyche introduced Jack Harrison, Beto and Arnaut Danjuma in a search for an equaliser that was simply too desperate and frantic. A series of aimless long balls made life easy for the promoted visitors who, despite the disruption to their defence, held Everton at bay comfortably in a second half featuring seven minutes of stoppage time.

Luton looked the more dangerous team on the counterattack and Morris was denied his second, and the team’s third, when applying the finishing touch to a header from an offside Jacob Brown.

“We had a brilliant chance today to change the story of the last two years and we didn’t do it,” said a despairing Dyche. “We are trying to create a mentality where the team is on it all the time. We have just taken two steps forward and now we’ve gone back again. It’s driving me mad.”