Is it possible to get a researcher position in a prestigious institute with a degree from a not very well-ranked university?
Yes, it is.

When you apply for a postdoc position several things will be important:


what you have done (i.e. does it fit with the future PI's research
agenda), 
how successful it was (i.e. did you publish your results
    in a top journal) and
you know what you want and you are burning for it


The name of the university might matter as well but once you graduated from your PhD your personal profile should be distinctive enough and the name does by far not matter as much as after your undergrads where everyone looks the same expect from the university name, marks average and some internship.