The game started at a high tempo, with both sides creating chances early on. Arsenal had the better of the play in the first half and deservedly took the lead in the 38th minute. Bukayo Saka played a lovely through ball to Havertz, who coolly lobbed the onrushing keeper to give Arsenal the lead.
The Gunners were seemingly in control of the game, but their task was made all the harder when Rice was shown a red card in the 50th minute. The midfielder was adjudged to have prevented a quick restart, and referee Simon Hooper showed him a second yellow card.
Brighton made the most of their numerical advantage and equalised in the 62nd minute. Joao Pedro fired home from close range after a good cross from Kaoru Mitoma.
Arsenal pushed hard for a winner in the remaining minutes, but Brighton defended well and held on for a deserved draw. The result leaves Arsenal still unbeaten in the Premier League this season, but it also means that they have dropped points for the first time.
The draw was a fair result in the end, and both teams will be pleased with their performance. Arsenal will be disappointed to have dropped points, but they will know that they have a tough game against Tottenham Hotspur next week. Brighton, meanwhile, will be delighted to have come away with a point from a difficult game against one of the title favourites.