In large skillet with high sides over medium heat, cook and crumble beef and onions until no longer pink; drain.
Add undrained tomatoes and 1½ cans enchilada sauce. Bring to a boil, stirring frequently. Stir in rice and ½ cup water; simmer 5 minutes, stirring occasionally.
Place ½ cup enchilada sauce in bottom of a 13x9-inch baking dish. Spoon ½ cup beef mixture down the center of each tortilla, top with ¼ cup cheese and roll-up. Place in baking dish.
Top with remaining enchilada sauce and cheese. Bake in a preheated 375°F oven 30 minutes or until cheese is bubbly and golden brown.