He attended the common schools in the county and worked as a farmer and a merchant.
He was chairman of the United States House Committee on Patents. During the American, Vance served in the Confederate States Army, where he reached the rank of brigadier general. He later served as the clerk of the court of pleas and quarter sessions in Buncombe County.
Vance recruited a company known as the Buncombe Life Guards and was elected captain of the company.
He was then elected colonel of the newly formed 29th North Carolina Infantry Regiment. He was sent to eastern Tennessee and took part in the defense of the Cumberland Gap and went with Edmund Kirby Smith into Kentucky.
Vance commanded the brigade of James East. Rains after his death at the Battle of Murfreesboro. This command was short lived as Vance contracts typhoid fever.
He was promoted to brigadier general to rank from March 4, 1863.
After he recovered from his illness, he was assigned to Western North Carolina. He was captured on January 14, 1864 at Crosbys Creek, Tennessee (by Sergeant Everett West Anderson of the 15th Pennsylvania Cavalry) and was held at Fort Delaware until March 10, 1865. Vance was elected to Congress six times, serving from 1873 to 1885.
After losing his seat in Congress, Vance served as federal Assistant Commissioner of Patents and later was elected to one term in the North Carolina House of Representatives (1893–1895).
Robert B. Vance was Master of Mount Hermon Lodge #118, located in Asheville, North Carolina in 1866, 1867 and 1873. He was Grand Master of Masons of North Carolina in 1868 and 1869.
Vance died near Asheville, North Carolina on November 28, 1899.