Swansea were the better team in the first half but paid the price for Bafetimbi Gomis failing to take advantage when put clean through by Jonjo Shelvey.
Arsenal were far from their best in that period, but Olivier Giroud put them on their way to a fifth successive Premier League victory four minutes after the restart with the 2,000th goal of Arsene Wenger's 19-year reign in north London.
If that goal was sheer simplicity, the unmarked Giroud heading home Mesut Ozil's corner, the second was shrouded in controversy as Laurent Koscielny bundled home after 68 minutes.
The former Arsenal goalkeeper Lukasz Fabianski failed to collect under pressure from Koscielny and Giroud, the sort of challenge which usually results in a free-kick.
But referee Kevin Friend felt no offence had been committed and Koscielny finished amid protests from Swansea players.
Joel Campbell wrapped up victory five minutes later with a clinical finish for his first Gunners goal as Arsenal eased to another three points.
It was the right Arsenal response to their shock Capital One Cup exit at Sheffield Wednesday in midweek and the perfect preparation for the crunch Champions League trip to Bayern Munich on Wednesday.
Wenger responded to midweek injuries to Theo Walcott and Alex Oxlade-Chamberlain by handing Campbell his first Premier League start and the Costa Rica international was prominent in the early stages.
Campbell set up Nacho Monreal's drive through a crowded goalmouth and then shot over after the ball had ricocheted into his path off Ashley Williams' shin.
But Arsenal were fortunate not to be behind after 21 minues when Shelvey brushed aside Ozil and slotted the ball through for Gomis to run onto.
Gomis had time to pick his spot as he advanced on Petr Cech but he hesitated and tried to take it around the goalkeeper, which allowed the pacey Hector Bellerin to get back and clear.
The chance, however, stirred Swansea into a period of dominance and Jefferson Montero slipped Bellerin to cross to the far post where Gomis headed straight at Cech.
Giroud spurned Arsenal's best chance of the half when, unmarked 18 yards out, he fired over.
Swansea had genuine claims for a penalty after 32 minutes
Gylfi Sigurdsson's free-kick was blocked by the Arsenal wall but referee Friend was unmoved, even though television replays appeared to show Per Mertesacker moving his hand to the ball
Shelvey headed over under pressure and Arsenal were content to get to the break on level terms, even if Campbell turned on Alexis Sanchez's pass to warm the hands of Fabianski.
But Arsenal stepped up the tempo after the interval and were immediately rewarded when Giroud peeled off Williams to head home his fifth goal in six games.
Sigurdsson replied with a powerful shot which Cech palmed away but Koscielny's controversial goal ended the game as a contest before Campbell added a third.
TWEET OF THE MATCH
"I think Arsenal could well win the league
There, I've said it." - Former Tottenham striker Gary Lineker (@GaryLineker) reacts to Arsenal's win.
PLAYER RATINGS
Swansea
Lukasz Fabianski 6 (out of 10)
Kyle Naughton: 6
Ashley Williams: 6
Federico Fernandez: 6
Neil Taylor: 6
Ki Sung-yueng: 7
Jonjo Shelvey: 7
Jefferson Montero: 7
Andre Ayew: 7
Gylfi Sigurdsson: 7
Bafetimbi Gomis: 6
Substitutes
Modou Barrow (on for Montero, 78mins): 6
Leon Britton (on for Ki, 84mins): 6
Eder (on for Gomis, 84mins): 6
Arsenal
Petr Cech: 7
Hector Bellerin: 7
Per Mertesacker: 7
Laurent Koscielny: 8
Nacho Monreal: 7
Francis Coquelin: 7
Santi Cazorla: 7
Joel Campbell: 7
Mesut Ozil: 8
Alexis Sanchez: 7
Olivier Giroud: 8
Substitutes
Calum Chambers (on for Giroud, 84mins):
Kieran Gibbs (on for Campbell, 84mins):
Alex Iwobi (on for Ozil, 90mins)
STAR MAN
MESUT OZIL: Took time to get into his stride but the German claimed two more assist for Olivier Giroud's opener and Joel Campbell's clincher
Sprang many of Arsenal's dangerous counter-attacks in the second period.
MOMENT OF THE MATCH
Campbell's excellent second-half finish came right in front of the delighted Arsenal following
But the game's turning point came when Bafetimbi Gomis was slipped through by Jonjo Shelvey and had the entire Arsenal half to run into
Gomis was closed down by Petr Cech but he should have shot, the chance lost when he tried to take it around the Arsenal goalkeeper.
VIEW FROM THE BENCH
Garry Monk named the same Swansea side which had ended their search for a first win in six at Aston Villa last week and was rewarded with a first-half display which was the most fluent for several weeks
But Monk was left to rue Gomis' first half miss and referee Kevin Friend failing to spot Per Mertesacker's penalty-box handball
Arsene Wenger might be bemoaning injuries to offensive players right now, but he knows he can count on Olivier Giroud as his fellow Frenchman has scored five goals in his last six games.
MOAN OF THE MATCH
Monk might wonder why Arsenal's second goal was allowed to stand
Laurent Koscielny appeared to back into his former Gunners team-mate Lukasz Fabianski, who was also coming under pressure from Giroud
In an age when goalkeepers are over-protected it's the sort of incident which normally yields a free-kick, but not this time as Koscielny was able to force the ball home.
WHO'S UP NEXT?
Bayern Munich v Arsenal (Champions League, November 4).
Norwich v Swansea (Premier League, November 7).
Source : PA
Source: PA