The visitors were the stronger side in the first half but failed to take their chances, and the Gunners hit them with two goals in quick succession after the break.
Alexandre Lacazette broke the deadlock against the run of play in the 55th minute with a fine curling finish that crashed in off the post.
Pierre-Emerick Aubameyang scored from close range just three minutes later, though the hosts were fortunate it was allowed to stand as the Gabon striker was well offside.
Arsenal's Attackers Are Hiding Cracks in Midfield, Defence
Arsenal managed to keep their first clean sheet of the season on Sunday, and manager Unai Emery will be delighted to see Aubameyang and Lacazette both get on the scoresheet.
However, the Gunners weren't particularly convincing for much of the contest and it's clear they're still a work in progress under the Spaniard.
Arsenal are continuing to pass the ball out from the back, which can be a rewarding tactic when done well, but they're struggling with the execution.
Granit Xhaka lost possession on the edge of the area more than once, not helped by team-mate Shkodran Mustafi, per Football.London's Charles Watts:
Next to Xhaka, Lucas Torreira made his first Premier League start. The Uruguayan could become a key player for the Gunners, but he was booked inside 15 minutes and was fortunate not to be sent off for foul on Lucas Digne shortly before half-time.
Arsenal's play in midfield was haphazard for much of the game, lacking rhythm or fluency, as the Evening Standard's James Benge and the Guardian's Jacob Steinberg noted:
With strikers as clinical as Lacazette and Aubameyang the Gunners will still be capable of winning many of their matches, but the team's overall play remains a long way off where they need to be.
Dominic Calvert-Lewin Not Ready for Premier League Starting Role
Dominic Calvert-Lewin has had a promising start to the season, netting three goals in his first five matches in all competitions.
Bleacher Report's Matt Jones was eager to see what the 21-year-old could produce on Sunday after being handed his third consecutive Premier League start:
The youngster struggled with the audition, though.
He had the chance to open the scoring after just two minutes when he was slipped through on the right, but his hesitation in pulling the trigger allowed Petr Cech to close him down.
The Liverpool Echo's Ian Doyle and Kyle Schnitzer of the New York Post weren't impressed:
Calvert-Lewin was eventually taken off after 71 minutes having failed to cause the Gunners much more trouble.
It's clear the forward has potential and he'll need time on the pitch to develop his game, but in the Premier League—particularly away from home and against those with top-four ambitions—he's not ready to make regular starting appearances.