Go to Start>Run
Type in DEVMGMT.MSC to open the device manager. Right Click your video card(s) and hit properties. Click the Driver Tab and click "update driver". If driver is already up to date or updating the driver does not work...
Is it one specific game? Have you tried other games to see if it crashes in them too?
If it's one specific game, try other games to see if it causes them to crash too. If not, completely uninstall then reinstall that game. If you've tried other games and it crashes all of them, I'm 99% sure it's your PSU. It takes a little while til the GPU is under full working load, and as your PSU gradually dies over the course of the next few months, it's crash after less and less time in games until you can't even get into them. Try replacing the Power Supply. I know you don't want to, but if the RAM is fine and you tried all the other stuff I said then PSUs the problem, and if it's under 2 weeks old it should be under warranty.