If we consider the sentence without the comma:
She walked slowly down the road evidently in pain.
It's confusing because
evidently appears to be modifying
road, since it follows
If we separate the two thoughts into their own sentences:
She walked slowly down the road. Evidently she was in pain.
This is, at least, clear; in terms of readability, the two sentences are a bit choppy, and it might read more easily and be considered to 'flow' better if they were combined.
She walked slowly down the road, evidently in pain.
The two thoughts fit together, the slowness of the walking explained by the evident pain.
I would regard this as a dependent clause; I don't know the exact grammatical structure someone would fit it to, but the comma is necessary and the sentence reads better than its two-sentence equivalent. The version without the comma reads badly and is confusing.