Arsenal manager Arsene Wenger was a satisfied man after his side upped their game in the second half in order to secure three vital points at Swansea.
The Gunners were subdued in a goalless first half but looked more lively after the break and eventually ran out comfortable 3-0 winners.
Olivier Giroud opened the scoring just after the break and Laurent Koscielny added a controversial second, before Joel Campbell wrapped things up with his first Arsenal goal in his first Premier League start.
Wenger said: "We didn't find our pace or rhythm in the first half.
"It's always a difficult game here and last season they took six points from us.
"We were a bit edgy coming here and the first half was very difficult for us.
"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.
"But in the second half there was tempo to our game and, after we scored the first goal, we were a different team.
"We knew that in the second half we needed to up our pace, our decisiveness, our determination.
"That came and I felt in the second-half it was one-way traffic. We dominated the game.
"I am happy for Joel [Campbell] because he works very hard. He has been very patient, so to come into the team and score, of course, helps his confidence."
Second-placed Arsenal have now won five Premier League games in a row and only trail leaders Manchester City on goal difference.
And Wenger is optimistic that they can remain in the hunt for the remainder of the season.
"We focus on our games and on our football and we are very ambitious and very hungry," he said.
"If we play like that, we will be in the fight.
"It is a very big week because we go to Bayern now [in the Champions League] and then play Tottenham at home.
"We have a number of strong results behind us. Let's keep a good balance between humility, hunger and team spirit."
Swansea felt their goalkeeper Lukasz Fabianski was fouled before Koscielny scored Arsenal's crucial second goal.
Wenger said: "I didn't see a foul, maybe I missed something and need to watch it.
"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."