Anichebe has been a key performer for the Blues this season, scoring seven goals and offering a series of muscular performances after shaking off a catalogue of injury problems.
Baines told evertontv: "We have known it for a while and believed in him for a while and he is starting to believe it himself.
"We are starting to see the rewards from that self-belief that he has gained.
"He has been an important player for us this season. He has come up with some important goals and beyond that he has given us something, with his strength, that we can play up to. Defenders are starting to fear him as well so he is a big asset to us."