The Gunners had by far the better of the contest and Nacho Monreal's first goal for the club gave them the lead with 16 minutes remaining, before substitute Gervinho struck in stoppage time. Swansea faded badly after a promising opening and, aside from a couple of half-chances, they barely worked Lukasz Fabianski in the Arsenal goal.
The win moves Arsene Wenger's side to within two points of fourth-placed Chelsea - and four of third-placed Tottenham - with their rivals in action on Sunday.
Arsenal could have led in the fifth minute thanks to Alex Oxlade-Chamberlain as he tricked his way past Angel Rangel to beat Michel Vorm, only for his shot to clip the top of the bar.
Swansea quickly settled after the early scare, and Ki Sung-yueng's weighted pass gave Rangel a run in on goal, but the full-back sliced wide of Fabianski's goal.
The hosts enjoyed an extended spell of pressure and the visitors almost gifted them an opener when Carl Jenkinson gave the ball to Jonathan De Guzman. The Dutch international fed Michu only for Swansea's top scorer to fire narrowly wide on the turn.
Santi Cazorla was proving Arsenal's most threatening attacking player and Vorm sharply saved the Spaniard's low shot after he had cut in from the right.
Michu was a peripheral figure as Swansea struggled to assert themselves and his poor day continued when he blazed miles over from Pablo Hernandez's smart pass. But Swansea's attacking forays were becoming increasingly rare and the dam eventually broke in the 74th minute.
Cazorla was again heavily involved as he tricked and teased his way past defenders on the edge of the box. The chance looked to have gone when Olivier Giroud took a heavy touch, but Monreal pounced to lash a shot across Vorm and into the corner with the help of a deflection off Ashley Williams.
Gervinho then made the points safe after Aaron Ramsey's pass teed him up to slot low beyond Vorm. Michu had to be restrained after an earlier disagreement with Fabianski spilled over after the final whistle, but nothing could take the gloss of an excellent Arsenal display.
Source: PA
Source: PA