I interview best when I'm relaxed and it doesn't feel like there's a lot riding on the interview. What has worked for me is to interview early (when I feel "maybe I should leave my current job", rather than "I have to leave this awful job ASAP or I'll lose my mind"). Even then, I've had bad interviews - where it's like forgetting your own phone number or PIN; It's hard to recover from your brain short-circuiting early on, I suspect my interviewers may have thought I'm a fraud too, but such is life.
Interviewing has plenty of randomness - on a few occasions, the stars were aligned and I solved sequences of very challenging technical questions much quicker than the interviewers had planned, which gave the impression that I'm some sort of genius. That performance was not representative of my usual capabilities, but I didn't tell them that (:
