Can the human body enter "Power Save" mode?
If you are performing the fast for ritualistic or spiritual purposes, then that mental state likely overcomes the feeling of thirst or hunger, especially if you are an otherwise healthy person. 

As for the physiological aspects. The Human Body is made up of 2/3 water, and as your kidneys are still functional, they are constantly filtering, and creating urine. The body can last a few days without water. 

As for food, the body has about a one day supply of sugar, assuming limited exertion, that it can consume before it begins to break down other substances. Then there are the fat reserves. The average person will likely have on the order of 7 to 15 kilograms of fat in reserve. There are 9 calories per gram of fat, so roughly 63 to 135 thousand calories worth of energy. Since the average adult will use about 2000 calories a day, then you can see that burning body fat alone would allow about a months worth of energy.

I am not saying that these are optimal conditions, but the body of a healthy human adult can easily withstand a 24 hour fast with no adverse effects. You would likely encounter more problems if you tried to go without sleep for the same period of time than if you refrained from food or water.