Antonio Conte and Arsene Wenger dropped key men as Alexis Sanchez and Eden Hazard started on the bench to be later introduced four minutes within each other in the second half. The shared points mean Chelsea sit behind the Manchester clubs in third on 10 points; while Arsenal relish in 12th on seven points.
Speaking afterwards Wenger said: "It was a game of quality and intensity all over the pitch and we battled well".
The result is also Arsenal's first point at Stamford Bridge in their last six visits, and also their first away point of the season.
Chelsea started the brighter of the two sides as Victor Moses got the better of Kolasinac to cross but Petr Cech was there to save.
"I think we needed that, after Liverpool", Arsenal midfielder Aaron Ramsey said. Alexandre Lacazette was in the right place for the rebound but he could not keep his effort from sailing over the bar. Fabregas had been unable to track the runners from the Arsenal midfield and the switch benefitted Chelsea's defensive structure. "I don't know. I would have to see that again on video".
Just like in the curtain-raiser to the season - when Arsenal beat Chelsea in the Community Shield - the west London cub finished with 10 men. Luiz let the ball get away from him and was chasing it before the Bosnian managed to get in ahead of him.
Danny Welbeck is facing yet another lengthy absence from the Arsenal team after limping off in the 73rd minute of their goalless draw against Chelsea with a suspected groin tear. The Blues face Nottingham Forest next in the League Cup at Stamford Bridge on Wednesday night.