A first half goal from Olivier Giroud and second half efforts from Laurent Koscielny and Joel Campbell kept the second-placed Gunners level on points with City.
Although Swansea had their moments, it was pretty much plain sailing for Arsene Wenger's side as they got back on track following their shock League Cup loss at second tier Sheffield Wednesday in midweek.
Wenger made seven changes to the side beaten at Hillsborough, including a first Premier League start for Costa Rica forward Campbell.
Having waited patiently for his chance, Campbell found himself in the thick of things early on as Arsenal quickly took control.
A far post cross, in the seventh minute, was only half cleared by Swansea leaving Nacho Monreal with a genuine chance to score.
Unfortunately, Monreal's shot was weak and wide of goalkeeper Lukasz Fabianski's far post.
The Gunners had to ride their luck minutes later when Jonjo Shelvey threaded a delightful ball into the path of Bafetimbi Gomis, who to the surprise of the Arsenal back four, found himself with only Petr Cech to beat.
But Gomis took too long in choosing an option and allowed Arsenal's Hector Bellerin to clear the danger.
- Golden opportunity -
Gomis, keen to make up for his earlier blunder, headed into the arms of Cech in the 21st minute and five minutes later Giroud should have done better when Santi Cazorla released him inside the Swansea area.
Giroud got a good connection, but the ball sailed high and wide of the target.
Shortly before half time, and having once again found themselves in a position of promise, Arsenal missed another golden opportunity.
This time it was Campbell who fluffed his lines from the edge of the penalty area.
Arsenal's frustration finally gave way to elation when they broke the deadlock four minutes into the second half.
Mesut Ozil whipped in a corner from the left and Giroud, who lost marker Ashley Williams with a degree of ease, headed firmly home.
Swansea's response was immediate. Gylfi Sigurdsson brought out the best in Cech, and then from 20 yards and from the ensuing corner, Cech had to stretch to clear a deflected header from Federico Fernandes.
Yet Arsenal regained their composure and made the game safe with two goals in the final quarter, albeit in somewhat controversial circumstances.
A deflected cross-shot from Bellerin should have been claimed by Fabianski at his near post.
However, the Pole flapped at the ball, lost his balance and gifted Koscielny the most simple of tap ins.
Swansea boss Garry Monk was clearly dissatisfied with referee Kevin Friend who he felt should have awarded a free kick.
Five minutes later, the game was over when Ozil crossed from the left for Campbell to control and beat Fabianski.
It was a special moment for Campbell after four years without an Arsenal goal.
Swansea huffed and puffed in the final 15 minutes but barely created a chance of note as Arsenal kept the pressure on City.