Cut carrots and rutabaga into 3-inch-long thin strips. Bring vegetables and 1/2 cup water to a boil in a saucepan; cover, reduce heat, and simmer 15 minutes. Drain and remove vegetables.
Melt butter in saucepan. Stir in sugar and next 4 ingredients; cook, stirring constantly, until sugar dissolves. Add vegetables; cook, stirring often, until thoroughly heated.