It was not only the victory, although that was plainly the biggest thing for Mikel Arteta and Arsenal, one to return them to the top of the Premier League table. It was the manner of it; how they absorbed everything that Brighton threw at them before pulling clear during a second-half masterclass of strength and control.

The success or otherwise of Arsenal’s title bid will surely be determined on the road and this was the first of four testing assignments – the others will come at Wolves, Tottenham and Manchester United. Brighton were unbeaten in their previous 14 matches in all competitions at the Amex Stadium; they were on a club record run of 12 top-flight home games without defeat. And for plenty of the first half, they showed why. They were slick on the ball, sharp with their movements. They asked questions.

Arsenal had the answers. The game swung in their favour in the 33rd minute when Tariq Lamptey decided to lunge in on Gabriel Jesus inside the area. Although the Brighton right-back nicked a tiny bit of the ball first, it added up to a penalty when he clattered into Jesus. Bukayo Saka’s conversion from the spot was firm and precise.

As for the second half, it was a message to Liverpool and Manchester City. Arsenal’s second goal had been trailed and when Kai Havertz, who was excellent in the No 9 role, scored it, that was pretty much that.

A red flare lit the scene behind the goal and Arsenal were not finished, easing to a 10th league win in 11 matches – the other game was the draw at City – when Havertz sent the substitute, Leandro Trossard, streaking clear. He faked to shoot, sitting down the goalkeeper, Bart Verbruggen, before clipping over him.

It had been a day when one former Brighton player – the right-back Ben White – shone in a powerful defensive collective. Now another, in Trossard, had twisted the blade. It was the prompt for thousands of Brighton fans to make for the exits. Their team had been dismantled and even Roberto De Zerbi was sitting down, the Brighton manager’s whirling dervish, technical-area act over.

The travelling Arsenal support loved seeing how their players mobbed Gabriel Magalhães when he made a stoppage-time block to preserve the clean sheet. And when they looked up at full time, they could see the most vivid of rainbows arching over them. Cue the pot of gold punchlines.

Brighton were badly hit by injuries but they had come to play, as always. The range of their passing was impressive at the outset and the statement of intent came on nine minutes with a sweeping box-to-box move, driven by Lamptey. It ended with Julio Enciso firing high. De Zerbi tried to target Oleksandr Zinchenko, Arsenal’s left-back, to get Simon Adingra one-on-one against him.

Arsenal had their chances before the penalty. Gabriel had missed a free header from Martin Ødegaard’s second-minute free-kick and Saka sparked a purple patch for his team in the 12th minute when he bent just past the far post. White had created the opening; he was in the mood. Jesus drew a fine save out of Verbruggen while the Arsenal forward erred when he headed square from a Havertz cross rather than go for goal.

The penalty was all about a split-second decision by Lamptey and it was one that he would surely not make again.

It was a challenge that showed his inexperience, according to De Zerbi; it was forceful and hugely risky. Nor was Jesus in an obviously dangerous area – on the left-hand edge of the box.

Arsenal’s quality on the ball shone brightly, their quickfire interchanges, especially in tight areas. Enciso had gone close to the equaliser on 44 minutes, shaping a curler for the far, top corner but David Raya was equal to it. It was all Arsenal after the restart.

White let himself down when he went down in exaggerated fashion, having felt Pervis Estupiñán put a hand in his face. Mercifully, the officials took no action against the Ecuador midfielder. White became the villain in the eyes of the home crowd.

Arsenal, though, stepped higher up the pitch. They increased the intensity. Ødegaard’s influence grew to the point where all he was missing was a conductor’s baton. Jesus headed wide after attacking a Havertz cross while Ødegaard worked Verbruggen and it was no surprise when Arsenal doubled their lead.

It was a goal to advertise the patterns that Arteta works so tirelessly to instil; the touches and the moves. Enciso played a loose ball, which was gobbled up by Jorginho and then it was White to Ødegaard and back up the inside-right channel to Jorginho, who had not stood still. Havertz darted for the near post; Jorginho’s low cross gave him a tap-in.

Trossard extended Verbruggen on 70 minutes and the goalkeeper would also save late on from Declan Rice. For Brighton, it could have been even worse.