You need to use a sorting subroutine which extracts the number that you want to sort by from the strings and sorts on that. It might look something like this:

#!/usr/bin/perl

use strict;
use warnings;

print sort my_sort <DATA>;

sub my_sort {
  my ($a_num) = $a =~ /(\d+)\.zip/;
  my ($b_num) = $b =~ /(\d+)\.zip/;

  return $a_num <=> $b_num;
}

__DATA__
{ID#0000D128}-20060519_090519_00000ZURACF2954.zip
{ID#0000D129}-20060519_091438_00000ZURACF2955.zip
{ID#0000D12C}-20060519_092458_00000ZURACF2957.zip
{ID#0000D12D}-20060519_092911_00000ZURACF2956.zip
[download]

Or there's a Schwartzian Transform version:

print map  { $_->[0] }
      sort { $a->[1] <=> $b->[1] }
      map  { [ $_, /(\d+)\.zip/ ] } <DATA>;
[download]

Or, if you don't care about maintainability :)

print sort
      { ($a =~ /(\d+)\.zip/)[0] <=> ($b =~ /(\d+)\.zip/)[0] }
      <DATA>;
[download]