The much-maligned Nigeria international has won over many doubters this season and his all-action performance in the stunning defeat of Manchester City a fortnight ago won widespread praise.
The 24-year-old has had his differences with Moyes, the club's hierarchy and fans in the past, while his career has also been punctuated by injuries.
But Moyes has kept faith and feels his patience is being rewarded with Anichebe, some seven years after his debut, starting to command a place.
Moyes said: "He is someone I have always thought has all the attributes, that if he could knuckle down and stick at it has definitely got a lot going for him.
"He has done. He has kept at it, kept going and I thought he played really well last time.
"His effort was noticeable. Victor, as much as anyone, helped us get the result against Manchester City.
"He was very close to being the man of the match, if he was not the man of the match."
Moyes feels Anichebe, an Academy product who has lived on Merseyside since infancy, has learned from his past difficulties and now realises how much potential he has.
The Scot said: "Maybe age, a bit of maturity - sometimes it does take players time for the penny to drop.
"He is a powerful lad and has an awful lot of attributes which he hasn't used at times.
"He lacks a little bit of self-confidence but the crowd can help him and it certainly helped him with the ovation he got against Manchester City.
"He is someone we have stuck with. There have been many times when he has been questioned."
Moyes wants more of the commitment and decisiveness the Toffees displayed against City to finish the season strongly.
The City result restored confidence at Goodison Park after the soul-destroying FA Cup quarter-final loss to Wigan and kept hopes of European qualification alive.
Their next challenge, at home, comes from Stoke on Saturday evening. The Potters have won just one of their last 11 league games but Moyes, without a win against Stoke since October 2010, takes nothing for granted against notoriously tough opposition.
He said: "It is the sort of game where you can get dragged into something somewhere.
"We have got to make sure we get the ball down and play, make passes and try to get through.
"Over the years we have done that against them, knocked at the door and still not got there.
"You have to be clinical and one (goal) is never enough. You have to make sure you get that other goal.
"We have had great form all year, so we have got to make sure we stay up there and finish in as high a position as we possibly can."