The fourth-placed Gunners moved four points clear of fifth-placed Manchester United with the win, on a weekend where only four league games will take place.
Arsenal had been beaten 2-0 at home by Liverpool last week, denting their top-four and Champions League ambition.
“It was a big win. After the defeat against Liverpool, but the performance that we had, we wanted to come here and play well first, which we did and get the three points,” Arteta told reporters.
“We want to keep the momentum going and I think the team showed today a lot of personality to come and play the way we played, the way we dominated the game and to come away with a win in the end.”
Bukayo Saka netted the winner with a 30th-minute strike although he was replaced in the second half with fears of injury.
“He was really fatigued as well, against Liverpool he had an issue with his hip, he’s played a lot of minutes and you could tell and we don’t want to risk it,” Arteta explained.
“He needs to go away with England now and we decided that the best thing to do was take him off.”
On Sunday, seventh-placed Tottenham and sixth-placed West Ham United can close the gap on the Gunners when they meet, while Leicester City host Brentford.