If your +12V voltage were really as low as Hardware Monitor shows, your system wouldn't even boot.
Try using a utility that actually knows how to interpret the signals coming from the motherboard's sensor chip.
Hardware Monitor is not the right utility.
The voltages displayed in your BIOS should be correct. If you find the right utility its displayed voltages should match the BIOS' displayed voltages.
I use AIDA64 Extreme Edition because I ran into the same problem you're having with wrong voltages being displayed in Hardware Monitor and Hardware Monitor Pro.
Another free utility I've used is HWiNFO64 v4.20-1960 available for download here:
http://www.downloadbestsoft.com/HWiNFO.html