Great advice as usual neuro. Noise will always be minimized by getting the brightest image you can get without blowing any highlights. One line of your response is what actually answers the OP...But, if you've got the aperture and shutter speed you want for the shot, you're better off bumping up the ISO in the camera rather than in post.
But why is that the case? In other words, why does the camera do a better job of increasing the exposure (by ISO setting that is applied after the exposure) than adjusting the exposure in post (DPP, DxO, LR, etc.)?
I'm not going to pretend i'm an expert at sensors, neuro may provide a better explanation, but I would have to say it's because the camera/sensor is the first to see and process the file and can do what it needs to do with those beautiful digic processors and sensor to provide the best image possible... where as when you do it in post, the computer is pretty much blind in the essence that all it "see's" is code and information of the digital file that your camera CREATED... Then when you do heavy post to it, it's amplifying the information of the digital file but basically it's creating information where information wasn't there to begin with, so your left with the noise as a result... It didn't/doesn't know exactly what was there so it does it's best to guess for you. It was kinda the same in film... you could underexpose and push the film in development or overexpose and pull the film, but it never was quite the same as nailing your exposure the first time... and even at that, like digital, you didn't want to push/pull your film more than 1 stop max unless you wanted some funky effects.
Ok, yes the RAW file as written to the card may have been already manipulated/processed and that could be an explanation why an ISO increase is superior to a post exposure increase, essentially that's what I'm asking... I don't know much about what is written in a RAW file vs. what the actual photosite measured values are, is there some data that is lost/changed/hidden/discarded by the time the RAW file is written. But I'll disagree that the camera's processor (DIGIC for Canon) can do anything an Intel CPU can do. DIGIC is in part optimized for certain Digital Signal Processing directly in hardware whereas your computer CPU is truly general purpose and relies on software so it is possibly slower but not worse.
I'm not saying that the digic can do miracles the intel CPU cant, but what i am saying is the digic, at the time of capture, can have access to information that the CPU just cant, such as information about how much light is hitting the sensor, any extra tidbits of information the sensor can pump out in certain areas, etc... The computer in dark areas just recognizes dark areas with little to no information in the dark areas, hence when you try to then increase the lightness, the camera is essentially guessing at what should be there whereas the digic doesn't have to guess, it just reads the information from the sensor and processes it directly in real time... no guessing really needed.