Exactly, you are sending the form to the server who will send back a complete page.
What you should do is have the new page contain the message that the form was successfully sent, or if there was a problem with the form (you do server-side validation, right?) -- give the details of the error.
For usability, it is important to make sure that you keep all of the form-fields you can. (E-Commerce fields are special, but keep everything else.)