The three points have moved the Gunners back up to fifth place in the table, while a third consecutive defeat has seen the Swans remain in ninth position.
Sports Mole delves deeper to take a closer look at the action from the Liberty Stadium.
On target 2
On target 11
Was the result fair?
While there was little to split between the sides in the first half, Arsenal's desire to get the win showed after the break and they ran out worthy victors.
Michael Laudrup's men started strongly, but by the final whistle their performance resembled that of a team who have nothing else to play for this season. Michu was particularly flat up front, even though he had some decent service from his teammates.
Despite riding their luck at times in the first half, the Gunners showed plenty of attacking intent when in possession and could have added to their tally in the second. There were some disappointing performances in attack from Olivier Giroud and Theo Walcott, but Santi Cazorla and Alex Oxlade-Chamberlain gave the hosts plenty to think about.
Sports Mole's man of the match
Santi Cazorla: The Spaniard was superb in the space between midfield and attack, making life extremely difficult for Swansea. He wasn't afraid to shoot when he had a sight of goal, and his calmness and incisive passing were a joy to watch.
There were no standout errors from either side during the match, but Swansea's fancy passing occasionally bordered on the excessive. It got them into trouble a few times and could have cost them a goal or two when they messed around on the edge of their own area.
Jon Moss had little to do all afternoon in a game between two sides who don't really do physicality. There were a couple of tasty challenges in the driving rain, but they were dealt with accordingly.
Swansea: The Welsh side will be eager not to make it three consecutive defeats in the league when they host Tottenham Hotspur next weekend.
Arsenal: The Gunners will be expected to get the three points when struggling Reading travel to the Emirates Stadium.