In most interviews there is a point in which you are asked about your future ambitions. Like, where do you see yourself 5 years from now? or What are your goals for your career? or something like that.
At that point you can mix the news of your pregnancy with your answer. I am sure that you have considered how your career will change with the new baby on board. Do you want to work more hours, or fewer? Do you want to take on a new project or scale back? Are you looking to change the direction of your career just a little to accomodate your life as a parent of a new little one? Whatever it is, you should be able to explain yourself pretty easily and truthfully while mentioning that you are pregnant.
I interviewed while I was pregnant, also around 27 weeks or so. You don't really show a lot, so people may not notice that you are expecting. So it really is important to say something, and early in the process as well.
I recall, after being asked about my future aspirations for my career, saying something like, "Well, I see myself doing more research. Currently I am 27 weeks pregnant with my first. So when I ready to return to work, I hope that I can be allowed time to begin delving into some research projects and also have enough time to balance work and personal life."
It is totally fair to hire someone while pregnant. It is NOT fair to not disclose a pregnancy until very late in the interview process or even after you are hired. I have helped my practice to hire, and believe me, this is unbelievably common! It really is so annoying and disrespectful. We need to stop being so skittish about the issue. If you are pregnant, so be it, and let the employers decide how they will handle coverage.