The match started in real end-to-end fashion and it was Arsenal who came closest inside the opening five minutes when Alex Oxlade-Chamberlain struck the bar with a side-footed shot from just inside the box.
Both teams were passing the ball well but there was a lack of a cutting edge, summed up when Oxlade-Chamberlain miscontrolled in the box with players waiting for the pass.
A few minutes later he cracked the woodwork again, this time on his right foot from distance, but the deadlock remained unbroken at half time.
Arsenal started as the stronger side in the second period and had a couple of early chances; a Cazorla shot was well saved before Abou Diaby's touch deserted him in the box before he could strike.
Then Hernandez was inches away from finding the corner as he cut onto his right and fizzed an effort just wide of the goal.
Arsenal started to get on top of the game with some good possession football, but there was a lack of creative spark as they were unable to carve out many chances.
That was until the Londoners broke the deadlock through the unlikeliest of sources as Nacho Monreal found the bottom corner with a scuffed finish.
Swansea almost drew level through a Jonathan de Guzman free kick, but his effort went into the wrong side of the net.
Gervinho made sure of the points in the last minute, slotting home following a swift counter-attack.