It was unbelievably easy, which was something I hadn't been expecting 'til that moment.
When he looked at me unbelievingly, I understood that he hadn't bought it.
When you modify a feature of something with 'unbelievably' you say that this feature is hard or impossible to believe in. Like in:
You're unbelievably beautiful.
The beauty of that person is hard or impossible to believe in.
'Unbelievingly' is an obscure word. It means more or less 'without believing' or 'not believing' (when it's used adverbially). Like in:
I just stared unbelievingly.
That person stared not believing in what he/she saw.