It was not only the victory, although that was plainly the biggest thing for Mikel Arteta and Arsenal, one to send them to the top of the Premier League table. It was the manner of it; how they absorbed everything Brighton could throw 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 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 much of the first half they showed why, looking slick on the ball, asking questions.

Arsenal had the answers. The game swung in their favour in the 33rd minute when Tariq Lamptey decided to jump in on Gabriel Jesus inside the area. Brighton argued loudly that he had nicked the ball first but the penalty was the correct decision. Bukayo Saka never looking like missing it.

As for the second half, it was a message to Manchester City and Liverpool. The 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 before 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 the substitute Leandro Trossard streaked away to finish nervelessly. Arsenal might have had even more before the end. Brighton had been dismantled.

Arsenal knew that it was essential they responded to Manchester City’s win at Crystal Palace earlier in the day and, after the fringe players move against Luton in midweek, Arteta went back to his A-team, recalling Declan Rice, Jorginho, Saka and Jesus.

Arsenal brought the numbers. No team has scored more goals in the league this season, or conceded fewer. They have been fortified by the taking of four points from each of their double-headers against Liverpool and Manchester City. It was about channelling the energy from it all.

Brighton came to play, as always. The range of their passing was impressive at the outset; ditto their movement. They mixed it all together in a sweeping ninth-minute move driven by Lamptey that ended with Julio Enciso firing high. It was a statement of Brighton’s intent. It looked as though they wanted to target Oleksandr Zinchenko on Arsenal’s left, and leave him isolated against Simon Adingra.

Arsenal had a flurry of chances in the opening exchanges that they did not take. As Brighton grew into the first half, it was possible to wonder whether the visitors would live to regret that. “You’ll mess it up,” the home crowd chanted – or words to that effect – although that was their more general prediction in terms of the title race.

The penalty came out of nothing; a split-second lapse by Lamptey that added up to a body blow for his team and a tonic for Arsenal. The Brighton right-back may have got a little bit of the ball but he got plenty more of Jesus, who had jinked inside. The challenge was forceful, and given the location of it – just inside the left-hand side of the area – hugely risky. It looked like a penalty in real time and, once awarded, the VAR saw no reason to overrule. Saka’s side-foot conversion was firm and precise.

Gabriel Magalhães had missed a free header from Martin Ødegaard’s second-minute free-kick – was the defender offside? – and Arsenal’s match was sparked by Saka, who cut inside and curled just past the far post. Ben White created the opening; he seemed in the mood to hurt his old club. Jesus drew a fine save out of Bart Verbruggen while the Arsenal forward erred when he headed square from a Havertz cross rather than go for goal.

There was plenty to like about Brighton before the interval. Carlos Baleba rampaged in central midfield and Adingra bristled with assurance. Enciso came close to the equaliser on 44 minutes, shaping a lovely curler for the top corner, but David Raya was equal to it.

It was fast and furious, the technical quality high, especially in tight spaces. There was needle, too, and White became the villain in the eyes of the home crowd soon after the restart. There was a coming together between the Arsenal defender and the left-back Pervis Estupiñán and, when the Brighton player raised his hand, White felt the contact on his face and crumpled – in exaggerated fashion – to the ground. Mercifully, the officials decided not to take any action against Estupiñán.

Arsenal stepped up a level. Their starting positions were higher; so was the intensity. Ødegaard’s influence grew. Jesus headed wide after attacking a Havertz cross and Ødegaard worked Verbruggen before Arsenal scored a second.

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 that was gobbled up by Jorginho. Then it was White to Ødegaard and back up the inside right to Jorginho, who had not stood still. Havertz darted for the near post; Jorginho’s low cross gave him a tap-in.