You can do that with two pipes and a fork.

my ($pread, $cwrite, $cread, $pwrite, $cpid);
pipe $pread, $cwrite;
pipe $cread, $pwrite;
select((select($pwrite),$|=1)[0]);  # added
{
    $cpid = fork;
    defined $cpid or die $!;
    last if $cpid;
    close $pwrite or die $!;
    close $pread  or die $!;
    open STDIN,  '<&'.fileno($cread)   or die $!;
    open STDOUT, '>&'.fileno($cwrite)  or die $!;
    $|=1;  # added
    exec $cmd;
    die $!;
}
close $cwrite  or die $!;
close $cread   or die $!;
# do your stuff
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There is also Open2 or Open3 if you don't want to do the dirty work yourself.

Remember to call waitpid $cpid; after you're done and the pipes are closed. Otherwise you get zombies.

Update: The output pipes should be set to autoflush. Added code marked.