Arsenal manager Arsene Wenger was delighted after the Gunners took all three points from Villa Park on Saturday.
The hosts started better with Fabian Delph and Ciaran Clark both forcing saves from goalkeeper Wojciech Szczesny but then lost concentration allowing the Gunners to strike three times in four minutes.
The win moves Arsenal to fourth in the table with nine points from five games.
"It was the response we needed after Tuesday," Wenger said during his post-match press conference.
"Aston Villa started quite well and they had one or two dangerous situations, but after that we were in control and we scored three goals in three minutes.
"Then in the second half it was a possession game, a controlled game, because they didn't come out too much.
"Overall it's still a convincing win where [Danny] Welbeck scored, [Mesut] Ozil scored, and that's important as well.
"He [Danny Welbeck] scored a similar goal to the one he scored in Switzerland.
"A cross from the left and he pushed it in - the timing of his run is good. I think he had a very good performance today because he kept the ball.
"Ball retention is important and he had a good all-round game for a central striker."