Código PHP:
$ch = curl_init();
curl_setopt($ch, CURLOPT_URL,"https://dental.dentalink.cl/sessions/login");
curl_setopt($ch, CURLOPT_POST, TRUE);
curl_setopt($ch, CURLOPT_POSTFIELDS, "rut=juan&password=1234");
curl_setopt($ch, CURLOPT_RETURNTRANSFER, true);
$remote_server_output = curl_exec ($ch);
curl_close ($ch);
print_r($remote_server_output);