Arsene Wenger admitted Arsenal had to overcome their Liberty Stadium anxiety before recording a fifth successive Premier League win.
Arsenal coasted to a 3-0 victory after Olivier Giroud had opened the scoring soon after the restart -- the 2,000th goal of Wenger's 19-year reign -- but it was a different story in the first period as Swansea threatened to inflict more agony on the Gunners.
Swansea beat Arsenal home and away last season and Garry Monk's men should have taken the lead when Bafetimbi Gomis was put through clean on goal but failed to beat Petr Cech.
Monk also felt Swansea should have been awarded a first-half penalty when Per Mertesacker appeared to handle Gylfi Sigurdsson's free-kick, but Arsenal were clinical after the break as a controversial Laurent Koscielny effort and an emphatic Joel Campbell strike maintained the pressure on leaders Manchester City.
"It's always a difficult game here and last season they took six points from us," Wenger said. "We were a bit edgy coming here and the first half was very difficult for us.
"But in the second half there was tempo to our game and after we scored the first goal we were a different team.
"I rested eight players on Tuesday [in the Capital One Cup defeat at Sheffield Wednesday] so it took us a while to get into the tempo of the game."
Koscielny doubled Arsenal's lead after 68 minutes despite appearing to back into Swansea goalkeeper Lukasz Fabianski when Hector Bellerin's cross was deflected into the air.
Fabianski was also challenged by Giroud but referee Kevin Friend felt no offence had been committed and Koscielny stabbed the loose ball home.
"I didn't see a foul, maybe I missed something and need to watch it," Wenger said. "The three points was the most important thing today and it was good to keep a clean sheet.
"It was a different game after we scored the first goal."
Swansea have now won only one of their last seven games and slipped one place to 13th on the back of this defeat.
"It's disappointing and we feel hard done by because there were a lot of positives," Monk said after a fourth home game without success. "In the first half especially we were the better team, playing good football and creating good chances.
"But the first two goals are disappointing and the mistakes we made you can't do against anybody, let alone a side with the quality of Arsenal."
Monk insisted Swansea were hard done by both on the Koscielny goal and the Mertesacker handball incident.
"I've seen fouls given pretty much every time when Fabianski comes, but the referee decided it wasn't and perhaps Fab could have punched it," Monk said.
"I've played in many games where whenever the keeper is touched a foul is given, but I don't expect things to go for us.
"I also knew it was handball at the time but I couldn't tell if it was intentional. But it clearly is, he moves his hand towards the ball to stop it.
"So I feel for the players because we were much better, much more like ourselves."