Chelsea came out 2-0 winners at the Emirates in a comfortable performance as Romelu Lukaku stole he headlines on his return to the club.
The Belgian put Chelsea ahead just 15 minutes in before Reece James doubled his side's lead before half-time.
The result means that Chelsea made it two wins in two London derbies at the start of the Premier League season.
It was the Gunners who registered the first shot on target within the first minutes. Emile Smith-Rowe's left-footed shot was held comfortably by Edouard Mendy in the Chelsea net.
Chelsea were ahead with their first shot on target and it was new boy Lukaku. The number nine did fantastically in the build up, holding the ball up and out-strengthening Pablo Mari to lay the ball off to Mateo Kovacic. A fantastic pass saw the Croatian pick out Reece James, who played a ball along the six yard box for the Belgian to tap in on his second Chelsea debut.
Since the goal, the Blues took full control of the match as Lukaku bullied the Arsenal defenders, showing his world class hold up play as Chelsea searched for their second goal.
Chelsea made it 2-0 with ten minutes to go in the fist half. Once again, Lukaku was part of the move. Kai Havert and Alonso combined cleverly before the Belgian dragged in two Arsenal defenders. The ball found Mason Mount, who picked out James on the right hand side of the Arsenal box. The full-back capped off a fine first half performance by putting Chelsea two ahead, firing into the roof of the net.
Arsenal grew back into the game at 2-0 down and had a penalty shout denied as Bukayo Saka fell to the floor following a challenge from James, however the referee waved away Arsenal protests and VAR did not overturn the decision.
The Blues took their two goal lead into half-time.
It was more of the same in the second half as Mount, Havertz, Lukaku and James were combining well.
A lovely piece of play on the edge of the Arsenal area saw the three forward men link up with some great one touch football before Mount unleashed a low shot that went just wide of the Gunnners' goal.
Lukaku continued his fine performance, backing into Mari as he received the ball before feeding Alonso, who played the ball back to James but the England international's shot was deflected over the bar.
Berd Leno pulled of a fantastic save to deny Lukaku a brace. Mount put an inch perfect cross into the 28-year-old, who headed powefully towards goal, however the Arsenal shot-stopper does well to react and make a reflex save and tip the strike onto the bar.
N'Golo Kante and Hakim Ziyech returned from injury in the second half, being given vital minutes whilst the Blues were 2-0 up.
Lukaku fed Havertz with five minutes to go and the German registered a shot on target from a tight angle but was unlucky not to beat his national teammate Leno.
Chelsea looked comfortable in defence as the Blues kept Arsenal out to take three points back to Stamford Bridge.