Sudden shutdown while gaming

I built this computer in April this year:

i5-2400 CPU
ASUS|P8Z68-V LE Z6 motherboard
8GB (2 sticks) CORSAIR CMX8GX3M2A1333C9 RAM
ASUS nvidia GTX 570 1280 MB GPU
Corsair TX750 750 watt PSU
DVD Burner from LG
Rosewill challenger case

The system operates beautifully except that it unexpectedly shuts down when playing certain modern games. It works for playing HD movies, playing some games (mainly older ones, though it has no trouble with some modern graphics-intensive games)The motherboard reports that the power supply is unstable; I turned off the power monitoring to see if the motherboard was shutting down the computer in error, but the computer continued to shut down while gaming.

The behavior is different for every game; generally, however, after 20 minutes to an hour, the computer shuts off, stays off for a minute or two and then restarts itself with the motherboard reporting an unstable PSU. I can generally boot it up and immediately play the same game for a little while before it shuts off again. This second round of gaming is usually a bit shorter than the first; the computer reliably shuts down the first time after about 30 minutes of Darksiders 2, for example, and then after 15 minutes or so every subsequent session unless I leave the computer off for a while.

The CPU and GPU never get above 50-odd degrees centigrade.

I do not have trustworthy components to swap in and test using the process of elimination, unfortunately, and I'd like some guidance on where the problem could be. My gut tells me I have a faulty PSU that craps out when the GPU or CPU asks too much of it (whether in watts or amps, I have no idea), but I have little experience in troubleshooting power problems.

I wanted to put this to you good people before I RMA (or outright replace) any components. I may pick up a 650 watt Antec Earthwatts PSU just to eliminate the PSU as a problem, btu I don't want to waste money if this is a mobo or GPU issue.

I've been building my own gaming computers for about a decade, but I have never encountered this sort of problem before.

Edit: Running Win 7 64bit professional. I've updated all my drivers for the GPU, CPU and mobo.