Technically intel suggests you don't run the processor above ~72 celcius. Now going over it a bit isn't really going to do much to it if it's only for a short while. If you run it at 80+ celcius 24/7 then you might see some degradation after some time(even then I donno), but it's nothing to worry about right now. I also don't think that would cause your computer to shutter. I was hoping that if prime95 would run error free for a couple hours it would help elimate the CPU as a cause.
Even with a stock heat sink those temps do seem a bit high. Are you running any overclock on your system? Also, do you mind opening hwmonitor again, turning on prime95 again for like 5 min and take a screenshot? I am interested in seeing what your voltages read.
To improve temperatures, you can try to reseat your heatsink, just make sure you have some thermal paste available before you start. If you find reseating doesn't help, and if you have a bit of spare cash lying around, I'd suggest getting and aftermarket heatsink:
Coolermaster Hyper 212 Plus Direct Touch 4 Heatpipe Heatsink AM2 AM3 LGA1366 LGA775 LGA1156 120MM
Can pricematch it on NCIX to $23.65
here. Fantastic price/performance, and that should help bring your temps down to more managable levels, and allows you to overclock a bit in the future if you choose too.