I cannot think of a way to do this with just the header() function but you could use cURL to send the POST data.
Then you don't even have to leave the page, i don't know if this is exactly what you were looking for but...
POST Example:
PHP Code:
<?php
$ch1 = curl_init();
curl_setopt($ch1, CURLOPT_URL,"http://www.example.com/page.php");
curl_setopt($ch1, CURLOPT_POST, 1);
curl_setopt($ch1, CURLOPT_POSTFIELDS,"x=hello&y=goodbye");
curl_exec ($ch1);
curl_close ($ch1);
?>
GET Example:
PHP Code:
<?php
$ch = curl_init();
curl_setopt ($ch, CURLOPT_URL, "http://www.example.com/page.php?x=hello&y=goodbye");
curl_setopt ($ch, CURLOPT_HEADER, 0);
curl_exec ($ch);
curl_close ($ch);
?>