It depends on the field. Some fields seem to be more concerned about undergraduate pedigree than others.
A UC Riverside Professor of Philosophy had a blog post on this topic a few years ago:
“Sorry, Cal State Students, No Princeton Grad School for You!”
“it seems to be extremely difficult to gain admission to an elite PhD program in philosophy if you’re not from an elite undergraduate institution.”
http://schwitzsplinters.blogspot.com/2011/10/sorry-cal-state-students-no-princeton.html