Put Texture on Object (Face) and bake it to use it on Unity?

Hey Guys,

I’m new to Blender and I’ve a problem with a Texture.
I want to put a Texture on the Face of a Character bake it to a new UVMap to use it in Unity.

When I put the texture on my Character without modifications it looks like this:

When I set Mapping to “Generated”, it looks almost perfect.

But I don’t know how to bake the UVMap (to image) so I can use it on Unity

When I put a second Material over the face for the painting, it looks like this :confused:

Could you help me out?