His best success came with the Atlanta Falcons, where he was traded prior to the 1972 season. In his first year with the team, Hampton surpassed the 1,000-yard rushing yard mark during the Falcons' final game of the season against the Kansas City Chiefs. However, he was tackled for a six-yard loss on the following play and ended the season with 995 yards. In 1973, he had another chance to get a 1,000-yard rushing season, but he ended up three yards shy. After missing most of the 1974 season due to injury, he rushed for 1,002 yards in 1975 and received the NFL Comeback Player of the Year Award.