In my experience it is the general rule (there may be exceptions) for companies which have HR do resume screening unless you have an in with the employer or manager.
That's usually the key point. I have a number of friends without college degrees that do just fine. Their usual modus operandi is to meet someone from the company at a conference, consult for them for a while, and then get hired once the company sees how awesome their work is.
I wish this weren't needed, but hiring managers function under conditions of very low information, and they wade through too many resumes of low quality to avoid filtering it on some criteria. Degrees and GPA are the most easily quantifiable filtering criteria, and so that's what makes it into the filtering software.
I think what's ultimately needed is a way to reveal more information about a candidates' abilities in a very short amount of time. Contract-to-hire works for this, but has the problem that many candidates (and in particular, good candidates) don't have time to devote to a project that may lead to a job. So does tokenadult's persistent suggestion of a work-sample test (and HireArt's implementation), but these both have the problem of being able to cut down an employee's daily duties into a small problem that can be given as a short task. Many of the skills that a really experienced employee brings to the table are only evident on long, hard, extremely challenging problems.