You will have to make the request from your PHP script. The curl extension enables you achieve this.
PHP Code:
$postVars = 'username=' . urlencode($username);
$postVars .= '&password=' . urlencode($password);
$curl = curl_init();
curl_setopt($curl, CURLOPT_URL, 'http://www.thesite.com/thepage.php');
curl_setopt($curl, CURLOPT_POST, 1); // make it a post request
curl_setopt($curl, CURLOPT_POSTFIELDS, $postVars); // add the post variables
$output = curl_exec($curl); // the response arrives here
curl_close($curl);