"php_mysqli does not replace the php_mysql library. It only extends it. You need the php_mysql library !"
mysql_connect() is from another library. Surely, php_mysqli works WITHOUT php_mysql enabled on the server. Nothing from php_mysql module is related to this.
Before switching to mysqli, you need to completely eliminate all "mysql_" functions in your code. For example, mysql_connect() could be replaced to mysqli_connect() with an identifying link in front. Like:
$link = mysqli_connect("myhost","myuser","mypassw","mybd");
Then each of mysqli command just should need to be referred to $link at first.