You have found the biggest weakness of WordPress. Unfortunately, it doesn’t have a simple solution (hence why there are so few search plugins, let alone good ones).
That said, you can look into Relevanssi (http://wordpress.org/plugins/relevanssi/), which is one of the better ones I’ve come across. It does allow you to search by field, but also installs some extra tables and adds a bit of server overhead.
If you’re running Apache, your best bet for a full-featured search is probably to install Solr and then integrate with WP (I remember seeing a plugin to help with this).
Good luck
