Wear something like this *underneath* your baseball cap:
Just push it up underneath the front of the cap and pull the cap down as far as it will go over your forehead. If the pad is too big, you can easily cut it down with some scissors. I have even see these sewn into the front of the cap liner.
I don't know what the technical term is for this kind of sweatband, but here's one example (that I got this picture from), but I've seen cheaper versions.