You can do this with the builtin module Time::Piece:

#!/usr/bin/env perl -l

use strict;
use warnings;

use Time::Piece;

my $start = '2013-10-28T18:59:52.863Z';
my ($whole, $ms) = $start =~ /([^.]+)(.*)Z$/;
my $t1 = Time::Piece->strptime($whole => '%Y-%m-%dT%H:%M:%S');

my $t2 = gmtime;

my $diff = $t2 - $t1;

print 'Whole seconds diff: ', $diff;
print 'Fractional seconds diff: ', $diff - $ms;
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Output (which is correct for my timezone):

Whole seconds diff: 46979
Fractional seconds diff: 46978.137
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My UTC date/time:

$ date -u
Tue 29 Oct 2013 08:02:51 UTC
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Confirmation calculation:

$ perl -E 'say(5*60*60 + 8 + 8*60*60 + 2*60 + 51)'
46979
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