Martin Odegaard’s early double put the Gunners in control and William Saliba added a third with his first goal for the club.
Odegaard had put Arsenal clear inside the opening 11 minutes, the first time the Norway international has scored twice in a match since playing for Stromsgodset in October 2014.
It is the first time in 18 years that Arsenal have started the season with three wins, and victory took them above north London neighbours Tottenham who had beaten Wolves earlier in the day.
Harry Kane kept Spurs on a Premier League roll as his historic header gave Antonio Conte’s side a 1-0 win.
The England captain struck from close range in the second half to score for the 185th time in the Premier League – the most a player has scored for one club in the competition.
Kane’s header took him above Sergio Aguero to fourth in the league’s all-time list of scorers and gave Spurs seven points from their opening three games.
With former Brazil striker Ronaldo in attendance at the Tottenham Hotspur Stadium, it was Kane’s 250th goal in all competitions for Spurs, with Jimmy Greaves’ record of 266 surely under threat this season.
His goal was also Tottenham’s 1,000th at home in the Premier League.
Fulham beat local rivals Brentford 3-2 in their first Premier League meeting, with Aleksandar Mitrovic claiming a last-minute winner at Craven Cottage.
Mitrovic headed home Kevin Mbabu’s teasing far-post cross after Brentford – who had two disallowed goals from Ivan Toney – fought back from being 2-0 down inside the opening quarter.
Toney saw two fine finishes ruled out for offside, only to make it what he thought would be third time lucky when he tapped home to level the scores at 2-2 in the 71st minute. Christian Norgaard had earlier pulled one back on the stroke of half-time.
But Mitrovic had the last word after earlier strikes from Bobby Decordova-Reid, inside 45 seconds, and Joao Palhinha after 20 minutes.
Wilfried Zaha’s double gave Crystal Palace a first win of the season as Aston Villa were beaten 3-1 at Selhurst Park.
Zaha swiftly cancelled out Ollie Watkins’ early opener before converting on the rebound after his second-half penalty was saved by Emiliano Martinez.
Substitute Jean-Philippe Mateta grabbed the clincher with his first touch 19 minutes from time.
Demarai Gray grabbed a late equaliser as Everton snatched their first point of the season with a 1-1 draw at home to Nottingham Forest.
Gray latched on to a long ball with just two minutes remaining to give the Goodison Park faithful something to cheer about.
Brennan Johnson had put newly-promoted Forest ahead just seven minutes earlier against the run of play.
Leicester, who were without Chelsea target Wesley Fofana, lost 2-1 at home to Southampton.
Substitute Che Adams’ stunning scissor-kick six minutes from time sealed Saints’ first victory of the season as Fofana watched from the stands.
Leicester took a 54th-minute lead through James Maddison’s free-kick, but Adams came off the bench to inspire Saints to victory.