The problem is most likely with your PSU not oyur monitor or GPU. Once your GPU hits higher loads it starts drawing more power, thus your PC shuts down or BSODs to prevent damage. You need a new PSU, I would suggest getting the Evga Supernova G2 550W. It will handle what you are dealing with right now, but if you continue like this you will probably damage your computer.
You think the PSU is the issue even if i can hold a skype call or continue to hear audio after it black screens?