Assuming that the page.php does exist in your root folder, as a physical file, then you can use:
RewriteEngine On
RewriteRule ^([^\.]+)$ $1.php [NC,L]
If page.php does not exists, but it is a product of a rewrite rule, you can use something like:
RewriteEngine On
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^([^\.]+)$ $1.php [NC,L]
The two extra rules say something: if file in browser does not exist and it is not an existing folder, then proceed with the rewrite.
You will need to change your links in your site, for the above rules to work. Something like:
<a href="http://www.example.com/page">Some fancy page</a>