I have had same issue and i misplaced some configuration.Firstly remeber that the user who created the php file can read the file and if the user who created php file is different than the apache user in your case it is apache
in that case you will get this exception if you try to write from different users.So what you have to do is simply,and i would suggest you to revoke the 777
permissions as i do not like idea of your files being publicity available on read and write to the world,so get it back to 755 and do the next on the command line of your server.
cd /var/www
change the user of the HTML only as we need it to be writable only,so do not touch the var and www,so basically as soon as you have navigated to he www directory you are going to change the HTML directory owner to the one who is currently running the apache server,and you got that info already,in your case it is apache
so we are going to do the next,
chown apache:apache html
At this stage the html file owner will be apache so you will be able to write onto it.Anyway and meanwhile i would strongly suggest you to create separate directory inside html lets say testDir
and try there,i would not suggest to change the root folder permissions,i had bad experience with them.Anyway i hope it will help as i suffer more then hour and just now got the right way to do it.This got my issue fixed,hope it will fix your's too.!