从AJAX响应中获取Cookie

Question

I'm writing a chrome extension that uses AJAX to talk to a server. I want to read the KEY in set-cookie from AJAX response, but I cannot find a way to do this.

I have tried document.cookie and xhr.getAllResponseHeaders()

$.get(myURL,
      function (output, status, xhr) {
          console.log(document.cookie); //empty
          console.log(xhr.getAllResponseHeaders()); 
          //Only Connection and Content-Type shows
      }
);

The raw response header is:

Connection:Close
Content-Type:text/html
Set-Cookie:KEY=DFDSFDCB; PATH=/;

I know that according to spec, getAllResponseHeaders() is supposed to filter out set-cookie field. Is there any workaround?