Have a look at Expect, it is written for exactly the situation you describe: drive an interactive program out of a perl program.

A solution could look like (straight out of the pod):

  # if you prefer the OO mindset:
  my $exp = new Expect;
  $exp->raw_pty(1);  
  $exp->spawn("./unrar", "e", $file);
    or die "Cannot spawn $command: $!\n";

  # send some string there:
  $exp->send("PASSWORD\n");
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Edit: reworded "would something look" to "could look", added pod-reference.