Arsene Wenger's side had lost both of their previous games on the road this season at Stoke and Liverpool, but might have picked up all three points at Stamford Bridge, as Aaron Ramsey struck the post in the first half and Shkodran Mustafi had a goal disallowed in the second.
Luiz was shown a straight red card in the closing stages of the London derby by Michael Oliver having been adjudged to have jumped into a challenge on Arsenal full-back Saed Kolasinac.
It is the third time in a row in which Chelsea have been reduced to 10 men against the Gunners, who earned a 0-0 draw at Stamford Bridge, but Wenger believes that the referee made the right call.
"It was excessive force, yes. I think Kolasinac was not completely on his feet. Even Luiz will accept there was a big distance and he went in too strong," he told reporters.
Chelsea failed to score in a competitive home match under Conte for the first time (27 games).