You probably want to take a look at the Expect module, which will let you handle the program as if you were typing it from the command line. Generally, sleeping like that isn't a safe way to go, as you have no idea whether the program is ready for input or not, and no way of verifying that the input it's prompting for is the input you're about to give it. Expect will let you wait for a certain prompt, such as (on my box)

(current) UNIX password:
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Alternatively, you could take a look at IO::Tty, and use it to set up a pty, which will make the passwd program behave as if you were sitting at a terminal, but this is basically what Expect is doing behind the scenes.

The problem you were running into may be related to OS buffering issues. You might try something like (code taken from Programming Perl):

select((select(ADD), $| = 1)[0]);
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which would turn on autoflushing on the ADD filehandle. I'd still recommend using Expect though, as it provides a much more robust and flexible way to accomplish your goal.

Update: I should have looked around a bit for this first, but you also might want to take a look at Unix::PasswdFile and/or Passwd::Solaris.