Heat a large nonstick skillet over medium-high heat. While the pan is heating, grate carrot. Add carrot, beef, and onion to pan; cook 6 minutes or until beef is browned and vegetables are tender. Add garlic powder, chili powder, and pepper; cook 1 minute.
Combine 1/4 cup ketchup and the next 5 ingredients (through tomato sauce) in a small bowl. Add ketchup mixture to pan, stirring to evenly coat beef mixture. Simmer for 5 minutes or until thickened.
While sauce thickens, arrange buns, cut side up, in a single layer on a baking sheet. Broil 2 minutes or until lightly toasted. Place about 1/4 cup beef mixture on bottom half of each of 8 buns; top each slider with top half of bun.