The Nigerian, playing his first game since August, came off the bench to net in the last few minutes in a match which his manager believes should have ended as a draw.
In a match of few chances, the Nigerian, playing his first league game since tearing a muscle in his groin on international duty in September, struck late on to give Everton the three points.
The 23-year-old made his long-awaited return to first team action in the fixture after suffering an ankle injury on the comeback trail, and has not even featured for the reserves.
“He’s someone who we’ve missed, he’s someone who’s got a lot of potential if we get the opportunity to unwrap it really," the Scot told reporters. “He’s missed a lot of football. At times he lacks a little bit of self confidence. I think the goal today and the reaction from the supporters will help him. Everybody likes it when you score the winning goal in a Premier League game."
The Toffees have only scored 19 times in 18 Premier League matches this season and nobody has managed more than three goals, but Moyes is hoping that he can slowly regain Anichebe's fitness and get him some more time on the pitch.
“He even felt tired after 25 minutes," Moyes said. "It’s going to be a case of gradually bringing him back on and getting him match fit.”
Anichebe was one of three players to come on inside the first 20 minutes of the second half as Moyes looked to revitalize an Everton side that was on the back foot.
One of the players to go off was Jack Rodwell, who had just come back from a hamstring strain, and Moyes said he had felt a tightness in the same hamstring.
The Everton boss felt that the three substitutes all had a positive impact on the game although, like his opposite number Roy Hodgson, he admitted neither side deserved to win a match where goalkeepers Ben Foster and Tim Howard did not have much to do.
“I think they did [deserve a draw]," he said. "We had to make sure the game wasn’t going to go in West Brom’s favor. They’d just started to get a wee bit more steam up in the second half and I wanted to alter it. We chopped and changed a little bit today but I think the subs had an impact in the game, both the boys. Victor obviously with his goal and Denis [Stracqualursi] as well.
"The game overall was a draw. I didn’t think there were many chances between either of the teams. We tried to make it difficult for West Brom like they make it difficult for teams."