Although the Gunners looked out of it for most of the first half, second-half goals from Olivier Giroud, Laurent Koscielny, and Joel Campbell secured the victory. Koscielny's goal, prompted by a borderline foul on/error by Swans and former Arsenal goalkeeper Lukasz Fabianski, and the score by Campbell in his first Premier League start were oddly fitting on Halloween.
Here are three things we learned from the match.
Mesut Özil is the Premier League's most dangerous man
We're still early in the Premier League campaign, but it's becoming clear that Arsenal's playmaker and record signing can push the Gunners to contend for the title. In the 10 matches Özil has played, he's tallied nine assists and created 47 chances, according to Squawka.
As 7AM Kickoff has pointed out in his "By the Numbers" articles for Arseblog, Özil has a real chance to deliver more than 20 assists this season. He's on an unreal pace of 0.96 assists per 90 minutes so far.
He picked up two more assists on Saturday, finding Giroud with a corner in the 49th minute, then working an intricate move with Alexis Sanchez on the left before fizzing a pass across the box to Campbell for the final Arsenal goal.
Özil also started the sequence that led to Koscielny's goal. When no Swansea player closed him down on Arsenal's right, he spotted the chaos in the Swansea penalty area and sent in the cross that Ashley Williams failed to clear properly. Fabianski, Giroud, and Koscielny were all waiting for the ball to come down, and Koscielny came away with it.
At the source of all these passages were Özil's ability to recognize the way to cause Swansea the most danger and the skill to execute the decisive play. It's a deadly combination.
Joel Campbell keeps the balance
A major question leading up to the match addressed the right attacking midfield position in Arsenal's 4-2-3-1 formation. With six more likely candidates for that role injured, manager Arsène Wenger gave a league debut to Campbell, who, despite some credible performances on loan and on international duty, had never shown he could reach the level required at Arsenal.
Campbell's calm finish, if not his celebration, certainly showed he belonged, but more than that, he slotted seamlessly into the existing Arsenal framework.
The Costa Rican helped move the attack forward, exchanging tidy passes with right back Hector Bellerin and the central midfielders. With Swansea understandably focusing on the threat Alexis posed on Arsenal's left, Campbell proved willing to take a shot when he had a sight of goal.
He also hustled to reach the right defensive positions. That was especially important due to the danger posed by the tricky Swansea winger Jefferson Montero. Although Montero caused a few nervous moments, Bellerin and Campbell managed the threat admirably.
Meanwhile, the rest of the Arsenal team could proceed as normal. In light of the successful recent performances, allowing his teammates to stick to their roles and strengths was Campbell's most important contribution.
Arsenal can survive risks and wobbles
This was as shaky a 3-0 victory as you're likely to see.
Particularly in the first half, Arsenal seemed vulnerable. The choice to use a high defensive line seemed overly risky given Montero's wiliness, the ability of Jonjo Shelvy and Ki Sung-Yeung to pick a pass, and the Gunners' struggles against Swansea last season.
The high line nearly proved calamitous midway through the first half, when Shelvy found Bafetimi Gomis and sent the striker clean through on Petr Cech's goal. Only the experience of Cech and the speed of Bellerin prevented Arsenal from going 1-0 down.
Giroud's goal early in the second half steadied things somewhat, but, even then, Arsenal made some odd choices. The defense was less coordinated and diligent than you'd expect from a team looking to protect a lead and counterattack. A few times Swansea players found space just outside the Arsenal area and took a crack at goal or nearly worked a teammate free.
Still, Swansea managed just eight shots on goal and only two in the penalty area. When the three Swans' shots did work Cech, he was more than ready.
The sixth clean sheet in 11 league matches--and the lowest number of goals conceded in the league--are evidence of the stability Cech has brought to the Arsenal defense.
Hector Bellerin doesn't just have a future; he has a present. As one-half of the league's best fullback tandem, the young Spaniard has brought quick interventions, sound positioning, and a real offensive threat to Arsenal's right side.
Against Swansea, he figuratively busted a gut to prevent Gomis from scoring and later literally busted one, throwing himself into the post to clear André Ayew's offside effort off the line.
Bellerin's contributions already and his clear talent warrant a long-term contract.