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.

DESCRIPTION
   The open2() function runs the given $cmd and connects $rdrfh for re
+ading and $wtrfh for writing.  It's what you think should work when y
+ou try

           $pid = open(HANDLE, "|cmd args|");
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use IPC::Run qw( run );
# just a silly command to execute in another process, to demonstrate
# how input, output and error all relate
my $command = q<perl -lpe 's/b/t/; warn qq{Oh, no!  A z in "$_"!  What
+ a world, what a world!\n} if /z/'>;

# but that way is sensitive to what shell you are using,
# (whether it is ok to use ' or " to quote in the shell)
# this way is shell-independant:
$command = ['perl', '-lpe', 's/b/t/; warn qq{Oh, no!  A z in "$_"!  Wh
+at a world, what a world!\n} if /z/'];

my ($in, $out, $err);
$in = "foo\nbar\nbaz\n";
run $command, \$in, \$out, \$err;
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------------
:Wq
Not an editor command: Wq
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using IPC::Open3 also catches STDERR, which is a good idea as well.

Depending on what command you're trying to run Expect may also be of interest.