The north London club scored twice within a minute in the first half, through Jack Wilshere and Olivier Giroud, before Christian Benteke pulled one back for the home side at Villa Park in the 76th minute.
Arsenal endured a difficult task in the second lot of 45 minutes as a buoyant Villa came at them hard but managed to hold out for a vital victory which saw them move ahead of second-placed Manchester City.
"In the first half, we were more about playing, and the second half we were more about fighting," he told Sky Sports.
"We got the answer, even if maybe we had some dangerous situations in front of goal. They made it very physical, put the ball high up in the air and played with three through the middle.
"We needed a very good, resilient performance in the second half."
Of Arsenal's title pursuit, Wenger added: "Let's take care of our performances.
"Then, you have to go forward always and get points, and see if you can make a difference with other teams."
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