Final answer:
The Patriot victory over Loyalists in Georgia's back-country was at the Battle of Kettle Creek. This engagement was significant in disrupting British efforts in the South and contributed to the ultimate American victory in the Revolutionary War.
Step-by-step explanation:
Patriot Victory in Georgia's Back-Country
The Patriot victory over Loyalists in Georgia's back-country was at the Battle of Kettle Creek. This battle occurred during the American Revolution, specifically as part of the southern campaign. After capturing Savannah, the British faced resistance from Patriot forces further inland. The Battle of Kettle Creek, which took place on February 14, 1779, was an important win for the Patriots. Led by Colonel Andrew Pickens, the Patriots defeated a force of Loyalists and helped to disrupt Britain's southern strategy. Despite early successes in the South, the British were eventually outmaneuvered by the Continental Army and the crucial assistance of French forces, leading to their ultimate defeat at Yorktown.
Other notable early battles in the revolution were Lexington and Concord, which marked the beginning of open conflict between the colonies and British forces. While the Battle of Savannah, mentioned in the student's question, was indeed a significant conflict, it was a British victory rather than a Patriot one, therefore not the answer to the query.