In a bizarre incident, the Arsenal midfielder earned a second booking for gently kicking the ball away and failing to retreat after fouling Brighton’s Joel Veltman.
Rice looked bewildered by the decision, while Arteta sought an explanation from the fourth official as Arsenal fans chanted “you’re not fit to referee” at Chris Kavanagh.
The Premier League said Rice was sent off for “delaying the restart”. VAR was unable to intervene because it was a yellow card and not a straight red.
Brighton took advantage of Rice’s dismissal to equalise through Joao Pedro, ending Arsenal’s 100 percent start to their bid to win the title for the first time since 2004.
The Gunners had won their opening two games of the season against Wolves and Aston Villa, but this was the first blow to their hopes of dethroning champions Manchester City.
Arsenal will be without the suspended Rice when they return to action after the international break with a north London derby trip to Tottenham on September 15.
Brighton extended their unbeaten run under new boss Fabian Hurzeler to three games as they followed up last weekend’s 2-1 win against Manchester United with another impressive display.
Arsenal new-boy Raheem Sterling watched from the stands following his deadline day loan move from Chelsea.
Sterling, who was frozen out by new Chelsea boss Enzo Maresca, wasn’t registered in time to feature but his name was cheered by Arsenal fans when he was welcomed to the club in a stadium announcement.
Rice sees red
Bukayo Saka tormented Brighton defender Jack Hinshelwood with his pace and movement in the early stages, easing into space for a pair of shots that Brighton keeper Bart Verbruggen repelled.
Ben White tested Verbruggen, who also denied Martin Odegaard as Arsenal swept forward in a red wave.
Arsenal were nearly punished for failing to turn their pressure into a tangible reward when Yankuba Minteh’s header forced a good save from David Raya.
But Arteta’s belief that the inconsistent Havertz can be an adequate striker for a team with title ambitions looked well placed in the 38th minute as the German broke the deadlock.
Havertz came in for criticism after scoring just 13 times last season following his move from Chelsea.
But he showed composure and quality to deftly chip over the on-rushing Verbruggen from the edge of the area after Saka punished Lewis Dunk’s hesitancy with a clever flicked pass.
Rice escaped with only a yellow card after the Arsenal midfielder crunched into Veltman, a decision that saw Brighton boss Fabian Hurzeler booked for protesting.
But Rice wasn’t so fortunate in the 49th minute when he was dismissed after kicking the ball away and failing to retreat before a Brighton free-kick.
Rice had just conceded a foul with a challenge on Veltman, whose kick out at the midfielder in the aftermath looked the more significant offence.
Pedro rubbed salt into Arsenal’s wounds with his 58th minute equaliser.
Dunk’s superb pass split the Gunners defence and Minteh sprinted clear for a shot that was pushed out by Raya to Pedro, who fired home from close-range.
It was the first goal Arsenal had conceded this season, but they should have regained the lead when Havertz broke free for a low shot that was too close to Verbruggen, who saved Saka’s sliding effort seconds later.
In a frantic finale, Raya saved Yasin Ayari’s close-range effort and Carlos Baleba smashed over the bar as 10-man Arsenal held on.
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