In a small bowl, mix together the tomato sauce, brown sugar, and mustard; stir until the brown sugar has dissolved.
In a large mixing bowl, mix the eggs, minced onion and green pepper, garlic powder, cracker crumbs, salt, and black pepper; mix in the ground beef and half the tomato sauce mixture, stirring until the meat loaf is thoroughly combined. Place the meat mixture into a 2-quart microwave-safe baking dish. Spread the remaining tomato sauce mixture over the meat loaf.
Cook in microwave oven on High setting until set, the juices run clear, and meat is no longer pink inside, 10 to 15 minutes depending on power of microwave oven. An instant-read meat thermometer, inserted into the center of the loaf, should read 165 degrees F (75 degrees C). Drain any grease from the dish as soon as loaf is cooked; allow to stand, uncovered, 10 to 15 minutes before serving.
