I will assume that your sponge balls did not come out of their packages with embedded hairs and that the hairs your are describing are the typical human/dog/cat/etc. hairs that one finds around one’s house. If either of these assumptions is incorrect, you’ll need to keep looking for an answer.
Mammalian hair generally has a layer of scales on it. On many animals, these scales tend to “face” one direction. Sponges (whether natural or manufactured) are porous–they not only have the holes that you can see, but their surfaces also have many smaller holes that are nearly invisible.
A hair landing on a sponge (or sitting on the floor and being fallen upon by a sponge) has some non-zero chance to have one end pierce the sponge’s surface through one of the tiny holes. At that point, the scales begin to act as the teeth of a ratchet, allowing the hair to move into the sponge when the surface is compressed, but preventing it from withdrawing . Once inside the sponge, the end of the hair may be deflected by the sides of the larger holes that make up that interior, so that the hair may begin curling about, further anchoring itself to the sponge.
Eventually, the hair is firmly caught within the sponge at one end, while the remainder of it may not have yet been “swallowed” by the sponge.
And, on preview, I see that Mangetout already answered, but since I’ve already typed this, I’m going to post it, anyway.