Some things are over-thought in dealing with women -- eye contact isn't one of them.
When you first make eye contact with a women -- do not glance away. Looking away is a habit many men have learned when dealing with other men. However, with women, I find by the time I glance back from my split second look over her shoulder, at her body, etc., she is no longer looking -- and probably won't the rest of the night.
You know how women say they decide in the first few seconds if they want to sleep with you? This is one of the prime ways how. Remember, in animals almost all information is communicated through the eyes.
Your first eye contact MUST not flit away for even a millisecond.
The best part of this tip is that it's easy to experiment with -- try it out and you will find a marked difference in the likelihood of her staring back, based on whether you flit your eyes after first making eye contact or not.
When looking at men, if you don't give the "breaking" glance, it seems threatening (or gay). We pick this habit up as politeness to other males.
However, women don't see it as threatening -- it will come back to (as all things do) a measure of your confidence. Stare her down -- or try.
I find that after a couple of seconds, it feels REALLY weird, and I smile and look away. (It's okay to let them win at this. Ultimately, in the game of attraction, they win anyway.)