Place the prime rib into a roasting pan, and rub all over the outside with the hot pepper sauce. Evenly sprinkle with garlic powder and Cajun seasoning.
Roast, uncovered, in the preheated oven for 20 minutes, then reduce heat to 350 degrees F (175 degrees C), and continue roasting to your desired degree of doneness, or an internal temperature of 145 degrees F (65 degrees C) for medium, about 2 hours. Remove from the oven, cover with a doubled sheet of aluminum foil, and allow to rest in a warm area 30 minutes before slicing.
While the roast is resting, scrape the drippings from the roasting pan into a skillet. Place the skillet over medium heat, and stir in the sliced mushrooms. Cook and stir until the mushrooms have softened and begun to release their liquid. Serve alongside the sliced prime rib.