Place corned beef, fat side up, and contents of spice packet in a large Dutch oven; cover with water, and bring to a boil over medium-high heat. Cover, reduce heat, and simmer 2 hours and 45 minutes or until fork-tender.
Skim and remove fat from surface. Add red potatoes and baby carrots. Bring to a boil over medium-high heat; reduce heat, and simmer 10 minutes. Add cabbage, and simmer 15 more minutes or until vegetables are tender.