This should work for you:
#example.com/page will display the contents of example.com/page.html
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteCond %{REQUEST_FILENAME}.html -f
RewriteRule ^(.+)$ $1.html [L,QSA]
#301 from example.com/page.html to example.com/page
RewriteCond %{THE_REQUEST} ^[A-Z]{3,9}\ /.*\.html\ HTTP/
RewriteRule ^(.*)\.html$ /$1 [R=301,L]