Yep except with MySQLi you need link identifyer I.E. when you connect you do something like
$Connection = mysqli_connect(...);
you would just need to use that in your insert query like
mysqli_query($Connection, "INSERT INTO MY_TABLE (NAME, EMAIL, PHONE) VALUES('bob', 'bob@bobssite.com', '555-222-111')") or die(mysqli_error($Connection));
$InsertID = mysqli_insert_id($Connection);
or if using the variable type class use
$Connection->query("INSERT INTO MY_TABLE (NAME, EMAIL, PHONE) VALUES('bob', 'bob@bobssite.com', '555-222-111')");
$InsertID = $Connection->mysql_insert_id();
=)