Nance was a 19th round selection of the Boston Patriots in the 1965 AFL Draft, as well as a 4th round selection of the Chicago Bears in the 1965 NFL Draft. Nance signed with the Patriots. Though his rookie season was unimpressive, he led the AFL in rushing the next two seasons. He went on to become the only AFL player ever to rush for more than 1,400 yards in a season. At 6-1 and 260 pounds, Nance was a powerful fullback who carried 299 times in 1966, for 11 touchdowns and 1,458 yards. That season, he rushed for 208 yards and two touchdowns in a 24–21 victory over the Oakland Raiders.