A smash-and-grab raid courtesy of a beautiful strike from Jarrad Branthwaite, pouncing on a second ball after a set piece: this was Dyche-ball in its purest form. As 90 minutes ticked by, its philosopher king, Sean Dyche, seemed set to celebrate another win over Roberto De Zerbi, the artful dodger denying the aesthete. Everton’s muscle and antics had caused Brighton to lose their discipline, Billy Gilmour sent off for a studs-up tackle on Amadou Onana.

But the problem with playing for time in modern football is that it is usually now added on. In the fifth minute of nine in stoppage time, Lewis Dunk, after skill and composure from the ever-dependable Pascal Gross, nodded in the first header Everton have conceded all season. “We pressed all game, then they went down to 10 men and we stopped pressing,” said Branthwaite.

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“We all know the drama around these minutes,” said Dyche. “Nine changes the atmosphere in the stadium and we didn’t deal with that well.”

Having not won in the Premier League since 16 December, his club might soon be relying on their lawyers. Everton expect an update by the end of the month on their appeal against a 10-point penalty. Their players must meanwhile perform in a purgatorial state of being. “We should be on 31, remember,” said Dyche. “Pretty healthy, it’s how you measure it. It’s my job to look at the bigger picture.” Such pressures eventually told.

This would be no free-scoring affair. Perhaps the team selections gave that away. Dominic Calvert-Lewin and Evan Ferguson, the starting strikers, had gone a combined 34 matches without a goal. Make that 36. Ferguson, withdrawn after Everton’s goal, is going through the growing pains even the best young strikers must see out – Alan Shearer, an admirer often compared to the teenager, was not prolific at Southampton – but here he was often far too peripheral in what became a desperate hunt for a breakthrough.

“He is not having the best time but we understand him,” said De Zerbi. “He can play better. We can help him. The team needs Evan on 100% of his physical and mental condition.”

As Danny Welbeck shot wide in the opening minutes, and then Jordan Pickford careered out to clear the danger from the same player, the guttural boom of Dyche bellowing touchline instructions underpinned the soundscape, as it did throughout. The plan was to sit back and seize on counterattacks and set pieces. A similar strategy was effective for David Moyes’s West Ham in August but Brighton had lost none of their 10 home league games since. Dunk, on his 400th league appearance, eventually extended that run. “It’s a valuable point on the table,” said Dyche, brusquely taking the positives rather than wallowing.

Calvert-Lewin had probably Everton’s best chance of the first half, only for a sharper-minded Dunk to get there first. By then, home fans were agonising over their team’s inability to convert dominance – 62% possession in the first half – and chances, the absences of João Pedro and Kaoru Mitoma keenly felt. Those frustrations grew after the break, with De Zerbi booked. A floor show was meanwhile being performed on the sidelines by Dyche and his assistants, a constant revolving pantomime dialogue with the fourth official, Dean Whitestone, as Everton deliberately slowed the flow of play.

On the hour, Tariq Lamptey headed Abdoulaye Doucouré’s volley from the line, the Brighton goalkeeper Bart Verbruggen already beaten, and Everton’s continuing danger at set pieces was confirmed by James Garner flashing a free-kick wide. Such warnings went unheeded. “The most important characteristic of Everton is the second ball,” said De Zerbi. “We worked on the training ground but maybe not enough.”

After Brighton brought on Julio Enciso ahead of a free-kick, their reorganisation failed them. Pickford launched the ball into the area, Ben Godfrey’s run took Gross and Ferguson with him before Branthwaite curled in a fierce shot. After Gilmour, perhaps unluckily but also correctly, was dismissed, Everton failed to relieve the pressure from 10 men. Gross, turning Beto inside out, showed a poise and incision his teammates had been lacking all afternoon. Dunk did the rest.