A four-minute spell in the second half proved decisive as goals from Serge Gnabry and the in-form Aaron Ramsey sealed an eighth consecutive away win in the league for the Gunners.
Ben Davies reduced Swansea's arrears in the 81st minute to set up a thrilling finale, but Arsenal held on to capitalise on dropped points from their rivals on Saturday and cement their position at the summit.
There was little in the way of goalmouth action in an uninspiring first half as the two sides cancelled each other out.
Jonjo Shelvey, back at the Liberty for the first time since his startlingly mixed performance against Liverpool, initially played a prominent part in a bright Swans start, his range of passing helping get the hosts in motion.
The midfielder also had the first meaningful effort on goal - one of very few during the opening 45 minutes - bringing down a high ball and fizzing a fierce drive narrowly over Wojciech Szczesny's bar.
Arsenal began to find their rhythm with Ramsey delivering a pinpoint cross for Per Mertesacker to head wide, before the Welshman arrowed a low shot around a yard wide from the edge of the area.
A lull followed, but Olivier Giroud should have had Arsenal ahead in first-half stoppage time.
Gnabry slalomed his way between three Swansea players to find the striker unmarked, but he dragged wastefully wide.
Gnabry was the man to finally force one of the keepers to make a save as he fired tamely at Michel Vorm five minutes after the break.
The German then gave the Gunners the lead as he rounded off a lovely, flowing passage of play with Ramsey at its heart.
The visitors worked Swansea from one side of the pitch to the other before picking them off through the middle as Giroud and Ramsey teed up Gnabry to shoot low beyond Vorm and become Arsenal's second-youngest Premier League goalscorer.
It should have been 2-0 a matter of moments later. Ramsey drove at the heart of the Swans' defence to find an unmarked Mesut Ozil, but Vorm stood up well to make the save.
But there was no reprieve in the 62nd minute. Arsenal again broke with purpose as Jack Wilshere and Giroud found Ramsey, who kept his cool to adjust and fire home, despite Vorm getting a hand to the shot.
Swansea had sent on Wilfried Bony between the two goals, but the Ivorian's introduction already appeared a case of too little, too late for the hosts.
Nathan Dyer forced Szczesny into a flying save, before Bony shot straight at the keeper after seizing on a Wilshere back pass.
They did manage to pull one back with nine minutes to go, Davies and Bony exchanging passes for the left-back to poke past an exposed Szczesny.
Arsenal had to survive a late penalty appeal when Bacary Sagna's attempted clearance appeared to strike Mathieu Flamini on the arm, but they were not to be denied another three points.