In cgi scripts, you need to worry about more than one instance running at a time. That requires locking, as well as the exclusivity you want:

my $path = "$dir/$name";
my $fh;
use Fcntl;
sysopen ( $fh, $path, O_WRONLY|O_EXCL|O_CREAT|O_EXLOCK ) or die $!;
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Update: Explicitly added Fcntl to get the symbols defined. Ahbeyra, please say what error messages you get, maybe post some more code.

Update2: Added O_CREAT flag. Props to jeroenes for spotting.

After Compline,
Zaxo