Beto struck twice, with Abdoulaye Doucoure and Iliman Ndiaye also on the scoresheet.
Moyes said afterwards: "What a result. It’s a great result for us all here at the Club. Just to get that feeling, two home wins now, and been up 3-0 at half-time in both.
"I'm trying to build on what's here and trying to improve the level of quality if possible, encourage the players, give them a bit of confidence.
"We want them to take the ball, we want them to try to play at the right times and I think that was evident today in moments. But, ultimately, I want them to score goals and I want to win and they certainly gave me every chance of having that feeling today. A goal after eight or nine seconds and then obviously we got a second one to back it up very quickly as well.
"There was one point in the second half where I was going to turn and look round because it was a bit like what I know it can be. It can be an intimidating place if you're the opposition, it can be a great place. I said today to the players before they went out, we need to feel the heat of Goodison and how we're going to get that is by us performing well.
"It was nice to see the smiling faces and everybody there right to the end watching the team. It’s a big thing.
"We've been desperate for goals. It was a brilliant pass by Jimmy Garner, I have to say, for one of Beto’s goals. And I just thought he'd done a lot of things which we're pleased about. Obviously, you know, there's things he’ll need to brush up on and improve as we go on. But I think today's performance was terrific from him coming in for the first time.
"I thought Jimmy Garner played really well today. He hadn't had much football back in training, you could see he'll need the games to get back but he made a big, big difference to us as well. So, great credit to the both of them."