Whilst I agree that having everything under one domain makes things simpler, one alternative is to use a subdomain, like blog.product.com. Then have productblog.com permanently redirect (301 response) to the subdomain. If you already have pages on the productblog.com domain, use a path mapping redirect, e.g.
Redirect ^(.*)$ http://blog.product.com$1 [R=301]
You should make sure that your primary site uses no www subdomain for its canonnical URLs, so that Google will say "see more results from product.com" (which will include blog.product.com) as opposed to "see more results from www.product.com" which would then exclude the blog pages.
Another suggestion if you use two domains or a subdomain is to add
rel="me" attributes on both linking to the other. This shows that you are in control of both domains and that they represent the real-world entity.