James Vaughan stepped off the bench to grab the winner with 10 minutes remaining after being set up by Victor Anichebe.
It meant Everton finished the group stages of the UEFA Cup with four wins from four games.
After seeing his team extend their unbeaten run to 13 games, Moyes said: "I am really pleased to come here and get a positive result.
"I did not tell the players about AZ's record. They did not need to hear it.
"But they were very pleased after the game to find out what they had achieved in difficult circumstances.
"It was very cold out there and a number of players were cramping up.
"While I was disappointed that we gave away a couple of cheap goals, we have to look on the positive side.
"We gave a number of senior players a run-out which was important given the number of games we have coming up.
"They all did well and so did they youngsters like Vaughan and Anichebe.
"We are all enjoying the experience and looking forward to the draw tomorrow."
