After just nine miles (14 km) of the stage from Augusta to Macon, Dan Bowman staged an early solo break in the rolling Georgia countryside to open up a 13 minute gap before the peloton reacted and began to reel in the 23-year-old rider.
He was absorbed back into the pack after 91 miles (146 km) alone and the peloton set up for a sprint finish in Macon.
Hunter surged to the front around 200 yards (metres) from the line to win the stage ahead of Australia's Ben Brooks and Italy's Michele Maccanti.
Thousands of spectators lined the route for Tuesday's stage to get a glimpse of Armstrong, who announced on Monday that he would retire after July's Tour de France.
It was an uneventful day for the 33-year-old Texan, who is using the six-stage Georgia tour as a tune-up for this year's Tour de France where he will chase an unprecedented seventh crown.
The second stage of the six stage Georgia race will be a 127.7 mile (205.5 km) dash from Fayetteville to Rome.