Wild celebrations in one small corner of an otherwise deserted Goodison Park told the story of a momentous day for Luton Town. For the first time since Brian Stein and Mark Pembridge scored in a 2-0 win over Aston Villa in April 1992 the Hatters had a top-flight victory to savour, and savour it they did after Rob Edwards’s resolute team brought fresh misery for Everton and Sean Dyche.

Goals from Tom Lockyer and Carlton Morris, both from Alfie Doughty set pieces, delivered a richly deserved debut win in the Premier League. Everton, meanwhile, picked a terrible day to lose a fourth consecutive home game from the start of the season for the first time since 1958-59.

Everton’s prospective new owners, 777 Partners’ co-founders Josh Wander and Steven Pasko, plus CEO Don Dransfield, were present to watch Dyche’s clueless team lose what can safely be described as another relegation six-pointer even this early in the season. A takeover can bring hope although another of 777’s clubs, Vasco da Gama, were hit with a Fifa transfer ban on Friday over the late payment of transfer fees to three other clubs.

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 to take the lead before compounding their problems at one end of the pitch with poor defending at the other.

Dwight McNeil volleyed a fraction wide from Everton’s first attack before James Garner, Idrissa Gana Gueye and Amadou Onana all missed the target from decent openings. Gueye’s was a particularly bad effort having been set up nicely by Onana and Abdoulaye Doucouré. Luton looked the epitome of a newly promoted team wondering where their first Premier League would come from. The quality of Doughty’s set-piece deliveries and the hunger to meet them eventually offered an answer.

Carlton Morris celebrates after scoring Luton’s second goal at Goodison Park.

Carlton Morris celebrates after scoring Luton’s second goal at Goodison Park. Photograph: Lewis Storey/Getty Images

Doughty’s first corner resulted in a free header for Lockyer that the captain steered over. The defender berated himself for the miss but did not have to wait long to make amends. Morris headed Doughty’s second corner against James Tarkowski and out for a third, which the towering Luton forward headed against Jordan Pickford’s 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’s inexplicable failure to leave 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.

Everton were in a panic and when Garner headed McNeil’s cross against the bar from only five yards out, in danger of becoming the first team in top-flight history to lose their opening four home games without scoring. That embarrassment was spared, at least, when Dominic Calvert-Lewin tapped in his third goal in three matches from a yard out after Luton goalkeeper Thomas Kaminski had denied Onana and Doucouré. A lengthy VAR check for offside against Onana and Calvert-Lewin eventually found in Everton’s favour and the floundering hosts had a lifeline. They lacked the composure and quality to capitalise.

Dyche introduced Jack Harrison, Beto and Arnaut Danjuma in a search for an equaliser that was simply too desperate and frantic. Luton lost three defenders, including Lockyer and Reece Burke, to injury, yet held Everton at bay comfortably while looking the more dangerous team on the counterattack throughout the second half. Morris converted Jacon Brown’s header back across goal but a third goal was disallowed for offside. There was no cause to rue the decision as Luton saw out seven minutes of stoppage time with ease.