Yes, there is way to use some of the Google Maps APIs to do this, but you don't necessarily have to invoke an actual map. I wrote a blog post about it back in November. The example in the blog post gets distance with coordinates as the starting location and an address for the final destination, but there's no reason they can't both be addresses.
Thanks, @jbante. This is just what I'm looking for. The distance "as the crow flies" works right out of the box on your solution. Unfortunately, I can't get the transit distance to work. I hit the little compass button, which I realized too late was the "get my location" button for iOS. So, I looked up my own coordinates and pasted them in those fields (- for west longitude or south latitude, right?). Again, the direct distance works fine. Either my internet connection doesn't work properly to call the web service, or something. I will check with my customer, maybe the straight-line method will be fine for them. They ship merchandise, and want approximate distance from our place to theirs. Thought road distance would be better, but I will see.
BTW, is there a way to send a parameter to get miles instead of meters? If not, easy enough to convert result.