The Gunners looked beaten when Jorginho fired Chelsea ahead from the penalty spot after Luiz was shown a straight red card for bundling over Tammy Abraham.
The Chelsea forward had pounced on a terrible backpass by Shkodran Mustafi and rounded keeper Bernd Leno when he was shoved over by Brazil defender Luiz.
Chelsea were dominant for long periods but failed to kill the game off.
They were punished when N’Golo Kante slipped inside the centre circle allowing 18-year-old Gabriel Martinelli to gallop free and produce a superb finish, the Brazilian becoming the first teenager to reach double figures in a single season for Arsenal since Nicolas Anelka in 1998-99.
It was Arsenal’s first shot of the game and came after a Chelsea corner which was cleared by Mustafi, the German atoning for his earlier error.
Chelsea thought they had won it when skipper Cesar Azpilicueta scored from six yards six minutes from time but spirited Arsenal earned a point through captain Hector Bellerin – making his first appearance since 5 December – from outside the penalty area.
Arsenal, who remain 10 points off a Champions League spot, have won just one of their last eight Premier League games and face the prospect of finishing outside the top six for the first time since 1994-95.
Mikel Arteta remains without an away win since taking charge in December yet his side played better with 10 men, and their gutsy second-half performance will have encouraged the Spaniard.
Luiz, who has given away three penalties in the Premier League this season – more than any other player – was left with little choice after Mustafi’s under-hit pass let in Abraham who looked certain to score after going around Leno.
Yet Mustafi made up for his error with the clearance which allowed Martinelli to burst forward, after Kante’s slip, and produce a sublime finish under Kepa Arrizabalaga.
Chelsea looked like they had secured a first top-flight double over their London neighbours in four years when Azpilicueta restored their lead in the closing minutes but Arteta’s side were not done.
Having dropped 13 points from winning positions in the Premier League this season, they showed a determination that has been missing and, with just their second shot of the game, Bellerin rifled in an equaliser to seal a fourth successive away league draw.