The Chilean has now scored five goals in three games for Arsenal and has 10 goals in total since arriving from Barcelona for £32m in the summer.
After the game, Wenger told BBC Sport: "It was a question of patience and quality and I think we did all of that. It was important not to concede a goal and in the end it was a comfortable win but everyone works hard in the Premier League.
"It was a top performance from Alexis Sanchez. His quality is exceptional, he takes responsibility and goes at people. He fights, he can score, that is what you want from great players.
"That [substitute] appearance form Theo Walcott gives him the confidence to play again. I think he will soon be back to his best level."
The win lifted Arsenal up to fourth in the Premier League table.