The duo both scored shortly after the restart, before full-back Ben Davies reduced the arrears in the final 10 minutes.
Below, Sports Mole has looked back over the contest to determine if the result was a fair one.
On target 3
On target 4
Was the result fair?
The statistics will tell you that Swansea had more of the ball over the course of the 90 minutes, but Arsenal made their share of the possession count. They also created the better of the chances and for those reasons, they were worthy victors.
As always Michael Laudrup's side were neat and tidy with the ball, but they rarely gave off the suggestion that they were going to hurt Arsenal. In short, they did not have enough of the possession in the final third of the pitch. At 0-0 that was fine, but they found themselves 2-0 down shortly after the restart and did not really seem to have an answer. They did apply some pressure after Davies had scored, but it was a case of too little, too late.
It would have not been surprising if manager Arsene Wenger did not give his side a rollicking at the break. Their key players were non-existent and their passing was wayward at best. To their credit, the Gunners were much sharper and positive after the restart and perhaps could have scored one or two more. In addition, when the time came to defend in the closing stages, they did so well. Wojciech Szczesny in goal also deserves praise for coming out to claim numerous crosses that had been lofted into his area.
Sports Mole's man of the match
Serge Gnabry: After what had been a rather pedestrian opening 45 minutes, the 18-year-old took it upon himself to liven the match up in the second half. He was positive every time he got on the ball and always looked to beat his marker when the opportunity arrived. The German capped off his performance by drilling in the first goal of the game form a narrow angle.
This can go to Jack Wilshere, who got lucky in the second half when he misplaced a pass towards his own goal. Wilfried Bony nipped in, but then hesitated over his shot, which allowed Szczesny to save. The relief on Wilshere's face was there for all to see.
One of the biggest compliments that you can pay Mark Clattenburg is that he was barely noticeable today. In fairness, Swansea against Arsenal was never going to be a bruising encounter full of feisty challenges, was it?!
Swansea: It's Europa League football on Thursday for Swansea as they play host to Swiss side St Gallen.
Arsenal: A tough night in the Champions League awaits the Gunners on Wednesday when Italian outfit Napoli visit the Emirates Stadium.