How do I get JSF to redirect to the default 401 page from within a managed bean?

Question

NOTE: I don't want to redirect to a custom 401 page, I just want to use the default one.

I tried following the answer in this question:

How to "throw" JSF2 404 error?

With the following code:

FacesContext facesContext = FacesContext.getCurrentInstance();
ExternalContext externalContext = facesContext.getExternalContext();
externalContext.setResponseStatus(401);
facesContext.responseComplete();

But it does not redirect at all. It just continues on.

I also tried:

externalContext.responseSendError(HttpServletResponse.SC_UNAUTHORIZED, "Page not found.");

But that did nothing either.

EDIT: I think the problem is that the redirection is not immediate. Before my code "returns" to the JSF lifecycle, it throws an exception.

Is there a way to redirect immediately rather than wait?