Both teams had opportunities to collect all three points, but neither could make the breakthrough as the spoils were shared following an entertaining contest in the English capital.
David Luiz, Victor Moses and Alvaro Morata were among those to return to the Chelsea XI, but Eden Hazard again started on the bench after only just recovering from an ankle problem. Pedro and Willian both kept their positions in the team, while Cesc Fabregas was preferred to Tiemoue Bakayoko in central midfield.
As for Arsenal, Arsene Wenger made eight changes to the team that started against FC Koln on Thursday night, with Nacho Monreal, Alex Iwobi and Hector Bellerin the only three players to keep their spot.
As expected, it was Chelsea that made the brighter start to proceedings, with Pedro stinging the palms of Arsenal goalkeeper Petr Cech inside an opening three minutes which were dominated by the home side.
Fabregas, making his third successive Premier League start, was next to come close for the Blues after meeting a near-post corner, but the Spaniard saw his effort deflected behind as Arsenal continued to look vulnerable.
The away side's first sight of the Chelsea goal came in the 16th minute when Bellerin found the head of Danny Welbeck with a brilliant cross from the right, but the England international missed the crossbar, before Alexandre Lacazette tested Thibaut Courtois with a low strike moments later.
Courtois then had to keep out a powerful effort from Sead Kolasinac as Arsenal showed signs of warming to their task. Chelsea were so dangerous on the counter, however, and Cech had to deny Pedro from a one-on-one in the 21st minute after a super pass from Fabregas had opened the Arsenal defence.
Xhaka swung one just wide of the Chelsea post in the 32nd minute as Arsenal continued to demonstrate their attacking abilities, before Welbeck had a goal-bound strike blocked by Chelsea's returning captain Cahill.
Arsenal really should have made the breakthrough in the 41st minute when Ramsey danced into the Chelsea box before poking the ball towards the far corner, but the Welshman's effort hit the post. The rebound landed straight to Lacazette, and the French striker somehow blazed into the stands.
Bakayoko replaced Pedro at the interval as Chelsea looked to regain control of the possession on home soil, and the Blues had a half-chance to take the lead less than two minutes into the second period, but Cech did well to save from Willian.
Arsenal continued to look dangerous on the counter-attack, but Chelsea were enjoying much more of the ball, with Morata looking to isolate German international Shkodran Mustafi in a wide position.
Willian was next to try his luck for Chelsea after working some space outside the Arsenal box, but the Brazilian international missed the far post as the score remained goalless entering the final 30 minutes of football.
Sanchez came off the Arsenal bench in the 66th minute to replace Lacazette, before Hazard replaced Willian for Chelsea two minutes later as both managers introduced their star players for the final phase of the match.
Mustafi thought that he had headed Arsenal ahead in the 75th minute after meeting a deep free kick, but the offside flag was raised as the centre-back's celebrations were cut short.
Hazard brought a smart save from Cech 10 minutes from time, before Fabregas tested the Arsenal goalkeeper as the score remained goalless at Stamford Bridge.
The frantic nature of the derby continued into the latter stages as both teams looked for the win, and Luiz picked up a straight red in the 87th minute following a late challenge on Kolasinac, but the score stayed 0-0 in the capital.
Both teams will now switch their attention to the EFL Cup, with Chelsea hosting Nottingham Forest on Wednesday, and Arsenal welcoming Doncaster Rovers on the same night.