It is necessary to integrate the Google Maps Geocoding API into the page.
First what you have to do is obtain a google maps api key, then you need to configure through scripts the call to the Geocoder api, where you pass the zip code and you will get a result with data such as latitude, longitude and formatted address that you can use to be able to fill in what you want.
It looks like you'll have to create a XHR request from the page embedding the form to any external geocoding service like Google Places API or so. Knowing that geocoding may lack precision.
Depending on embedding page, it could be tough to accomplish, but integration essentially consists of listenning form events to trigger geocoding task. For Wordpress based sites, Leadin extension allows usage of form hooks easily.