The 24-year-old made his comeback after two months on the sidelines with a goal in last weekend's come-from-behind win at West Ham.
With Kevin Mirallas, arguably the Toffee's best attacking outlet this season, struggling with a hamstring injury Anichebe's return could not have been timed better.
"Victor has played very well. He is an important player for us and a lot people under-estimate what he can do for us," said Moyes.
"Not having him available means we have not been able to change many things in the attacking areas.
"Not having Mirallas available for the last couple of months at different times has meant we have been limited in forward areas and probably not won as many games as we should have.
"We want to keep him (Anichebe) fit and him to have a bit of self-confidence and I am sure that goal will do that for him."
Everton host bottom-three side Wigan on Boxing Day without midfielder Marouane Fellaini, who serves the second of a three-match ban for headbutting Stoke's Ryan Shawcross.
In the Belgium international's absence Leon Osman stepped into the pivotal position in the hole behind striker Nikica Jelavic and Moyes said it was testament to the 31-year-old's quality he slotted in there seamlessly.
"He has been very under-estimated over the years but now he is not," added the Scot.
"He has recently been selected for England and some of his performances have been terrific.
"He has taken on a lot of leadership jobs now, he is a good lad around the place and is a big part of the team and a big part of how we want to play.
"It was great he moved out of position on Saturday and was terrific and arguably he has been one of our best players of the season."
Everton will have Darron Gibson available to face Latics despite the midfielder's red card at Upton Park as an appeal is pending.
Gibson was dismissed by referee Anthony Taylor for a challenge on Mark Noble but as the Football Association require two working days to deal with an appeal, the Republic of Ireland international has had his ban suspended until his case can be heard later this week.
"We think there's a real reason to ask the FA to re-look at it," said Moyes, who believes Wednesday's opponents have not had the credit they deserve despite being in the bottom three.
"Roberto has done a really good job there, he has a good technical side and they are a test for all teams.
"Folk think their league position is a guide but I don't think so, I think they have played some good football and we will have to do all the right things.
"You always want to come out of the Christmas period being no worse but if you can do better than your league position was when you went into it then that is great.
"It is an important time and once you come through this you are into January and you know the finishing line is in the distance."