I would support the earlier advice of the esteemed monks to use Archive::Zip module as it provides a fairly easy and straightforward way to zip files.

Here is a function that I use in my scripts (it might be not the best way to do it, but it works...)

sub ZipFile($)
{
   my $fname = @_[0];
   my $error = 0;
   
   my $zipfile = $fname.'.zip'; #Update filename, add .ZIP at the end
   my $zip = Archive::Zip -> new();

   my $member = $zip->memberNamed( $fname );
   if ($member eq undef) #No existing zip file with the file inside
   {
      $member = $zip->addFile( $fname ) or $error = 1; #Add file to ZI
+P archive
      push @ERRORS, "Unable to zip $fname: $!\n" if $error;
      LogError() if $error; 
   }

   $member -> desiredCompressionLevel( 9 );
   my $status = $zip -> overwriteAs($zipfile);
   
   push @LOG, "$fname compressed (zipped) successfully\n";
   return $zipfile;  #Return updated filename
}
[download]

The function attempts to create a new .ZIP file, and 'add' a text file into the archive, thereby doing the same thing that you do when using Winzip to compress the file.

Hope this helps :)