The visitors took a shock lead through Sam Clucas mid-way through the first-half and despite enjoying 78% of the possession for the rest of the opening period, Arsenal could not find an equaliser.
They did, however, hit back through Sead Kolasinac and Aaron Ramsey in the second 45 to take all three points in Arsene Wenger’s 800th Premier League game in charge of the Gunners.
In a rather lethargic start to the game, it was Arsenal who looked most likely to take the lead. Alfie Mawson had to block fierce strikes from Alexis Sanchez and Hector Bellerin to prevent Wenger’s side from opening the scoring. Sanchez also saw an audacious strike from range fizz wide early on.
Swansea, who looked dangerous on the counter throughout the first period, took a shock lead on 22 minutes following a delightful through ball from Tammy Abraham. Clucas beat Bellerin to reach the pass and coolly tucked under the onrushing Petr Cech.
Sanchez came close to an equaliser after neat link-up play with Mesut Ozil, who back heeled into the path of the Chilean, but his fierce strike was well pushed away by former Arsenal stopper Lukasz Fabianski.
Swansea should have doubled their lead just before the break when Per Mertesacker’s poor defensive error allowed Jordan Ayew in on goal. The striker, however, couldn’t clip over Cech.
Arsenal did draw level quickly after the restart through Sead Kolasinac. Alexandre Lacazette’s backheel found Ozil, whose shot was blocked into the path of the defender, and he rifled it into the corner from the left of the box.
The Swans thought they had an immediate response when Abraham had the ball in the net, but he was offside following a scuffed shot from Clucas.
Ramsey completed the turnaround on 58 minutes with a trademark Arsenal goal. Granit Xhaka’s crossfield ball was well controlled by Kolasinac and he cut back for the Welshman, who calmly tucked home at the near post.
The Gunners could have made it three when they broke following a Swansea corner with just over 20 minutes to play. Ozil switched the play to Ramsey, who threaded a ball through to Bellerin, but his touch on the stretch hit the top of the bar.
Swansea pressed for an equaliser but the closest they came was a an effort on the turn from Abraham, which flew just wide of Cech’s post.
Arsenal closed out the game with relative ease to secure all three points, but that’s now two games in a row in which they they have fallen behind early on. Paul Clement will be able to take positives from his side’s display, but they remain just above the relegation zone with eight points from ten games.