I think utilize goes a little farther, it implies using something to its fullest extent?
I understand it to mean "to use something for a purpose for which it was not originally intended". My favourite example is that I use a garlic press in the kitchen, but I also utilize one in the studio to shape clay.

As for your thought, AnnaS, I once suggested to a fellow who told me this same definition:
"So if someone has sex with you once, you've been used, but if they have sex with you three times, you've been utilized?" He didn't get it.