Something like this:

if (fork() == 0)
{
  close STDIN;
  close STDOUT;
  close STDERR;
  do_long_running_thing();
  exit 0;
}

print_out_web_response();
[download]

Now, granted, I missed a bunch of error conditions around fork, as well as omitting the Highlander Maneuver, but that's the basic idea.

Note that you can reopen stdout and/or stderr and redirect them to a file, or you can pipe them into something that'll send you an email, whatever you want. If nothing else, you may want to reopen to /dev/null, just to sure you don't confuse subprocesses if you call any.