David Luiz was red-carded as three minutes from time as the Blues could not force their way past a resolute Arsenal in the early afternoon kick-off at Stamford Bridge.
The 0-0 draw was just about correct but the visitors can claim to have had the better of the chances - Aaron Ramsey hitting the post.
This was a below par performance by Chelsea and Arsenal can take credit for their tactical nous which smothered the Chelsea midfield and reduced creative players Cesc Fabregas and N'Golo Kante to bit players.
Luiz, up, until the 87th minute was Chelsea's star man, but under pressure from Alexis Sanchez, lost the ball and lunged out onto the shin of Sead Kolasniac. Referee Michael Oliver did not take time to think about it, and decided straight away it was a dangerous tackle and thus brandished the Brazil defender with a straight red card.
Chelsea started brightly, forcing ex-Chelsea goalkeeper to be alert to a low drive by Pedro. A succession of corners however failed to yield the early breakthrough.
On 15 minutes a misjudgement by Gary Cahill allowed Arsenal to counter-attack with one-two precision, resulting in Danny Welbeck to head just wide. Alexandre Lacazette, then forced Thibaut Courtois into a smart low save from close Range and the visitors cut the Blues apart.
Sead Kolasinac then had a powerful shot, which Courtois did well to parry out of harms way.
Pedro, back on the pitch after a painful challeng poleaxed him, was sent clear by Cesc Fabregas, but the Spanish live-wire could not get past Cech.
A blistering left footer by Granit Xhaka, on 32 minutes looked spectacular, but Courtois tracked the ball and knew early that it was zipping wide of goal.
Quite how Arsenal failed to score with four minutes of the half remaining is an understatement First Aaron Ramsey raced straight through the Chelsea rearguard but saw his shot, rebound off Courtois left post. In-running Lacazette should have rammed the ball home but somehow mistimed the ball and skied it over the crossbar.
Chelsea replaced Pedro at half-time with Tiemoure Bakayoko suggesting he was not happy with the midfield composition, which, to be fair, Arsenal bossed for the previous 20 minutes.
Willian had a shot on goal, within a minute of the restart - Cech easily snaffled the shot.
The game entered a fallow period with neither side looking to risk a chance.
Eden Hazard entered the fray with 21 minutes on the clock replacing Willian.
Arsenal thought they scored on 75 minutes when Shokodran Mustafi headed past Courtois from close range, by he was offside from the fre-kick.
Cech thwarted substitute Eden Hazard on 80 minutes, when the midfielder raced through the Arsenal defence and let fly from the edge of the penalty area.
With three minutes left, David Luiz, under pressure from Sanchez, lunged into Kolasinac and referee Michael Oliver brandished a straight red.
Conte instantly replaced Morata with centre-back Andreas Christensen.
The Blues were quite happy to see out the remaining minutes to take the draw.
Teams: Chelsea:
Courtois, Moses, Azpilicueta, Luiz, Cahill, Alonso, Kante, Fabregas, Willian, Pedro, Morata
Subs: Caballero, Christensen, Rudgier, Hazard, Bakayoko, Zappacosta, Batshuayi
Arsenal: Cech Mustafi, Koscielny, Monreal, Xhaka, Ramsey, Bellerin, Iwobi, Welbeck, Kolasinac, Lacazette
Subs: Ospina, Mertesacker, Sanchez, Giroud, Walcott, Maitland-Niles, Elneny,
Referee: Michael Oliver