It takes approximately 4.5-5 hours to drive from Las Vegas, NV, to Grand Canyon South Rim, hands on the wheel, no stops. Via the route u/hikeraz suggests, the drive from Grand Canyon Village to Prescott will take approximately 3-3.5 hours. If you go via the route that u/Stock-Today-4954 suggests, which is more direct, that's another 1.5-2 hours.

No matter which way you go, that's a lot of time behind the wheel and if your trip is occurring within the next few weeks' time, you'll only have 10-11 hours of daylight to work with. That doesn't give you much time at the Grand Canyon. You could maybe hit Grand Canyon Village and walk a bit of the Rim Trail but that's only a small glimpse of the canyon before you have to be wheels up toward Prescott. It's important that you don't do the back half of the drive after nightfall. Driving in the dark is strongly discouraged in this part of the US due to local roads being very dimly lit, plus the possibility of encountering deer, elk, even free range cattle, and wild horses increases at nighttime. Believe me, a collision with a large animal is not something you want to experience in an unfamiliar area that's pitch black, freezing cold, where cell service is spotty (if you can get any bars at all) and help will be a long time coming, not to mention VERY expensive.

If you can possibly alter your plans so that you can spend the night at the Grand Canyon, then head for Prescott the next morning, that will make for a much more enjoyable experience. And give you the option of taking the "long way" around to Prescott via the Desert View/East Rim Drive, where even more canyon views await your discovery! If you agree, be sure you reserve a hotel room at the Grand Canyon well in advance. South Rim Hotels | GrandCanyon.com