Diego Guajardo's 34-yard field goal was the only score in the first quarter as South Alabama took a 3-0 lead.
Barnett's 2-yard TD run was the only score in the third quarter and stretched Georgia State's lead to 21-3.
Ellington's 4-yard scoring toss to Roger Carter pushed the Panthers' lead to 28-3 just 7 seconds into the final period.
Ellington finished 21-of-28 passing for 208 yards with one interception for Georgia State. Carter finished with seven catches for 87 yards.
Trotter completed 12 of 25 passes for 218 yards with a pick.
Power 5 commissioners fear different compensation rules for different states
Stadium Network's Brett McMurphy discusses the Power 5 conference commissioners wanting Congress to proceed with legislation about compensation for college athletes.
Hall of Fame RB Floyd Little, who starred for Broncos, Syracuse, diagnosed with cancer
Running back Floyd Little, who starred for the Denver Broncos after a standout career at Syracuse, has been diagnosed with cancer. Little, 77, is a member of both the Pro Football Hall of Fame and the College Football Hall of Fame.
Muschamp details plan for when players return
South Carolina head coach Will Muschamp joins The Paul Finebaum Show and shares how his staff will handle the players when they begin training for the season.
Governors, Vandy AD weigh in on The Paul Finebaum Show
Five Minute Finebaum: Tennessee Gov. Bill Lee, Mississippi Gov. Tate Reeves and Vanderbilt athletic director Candice Storey Lee partake in important discussions.
College Football Hall of Fame damaged by protesters
The College Football Hall of Fame was damaged and looted during violent protests in Atlanta on Friday night, police confirmed in a statement.
College Football HOF damaged by protesters
Mark Schlabach reports the latest on the College Football Hall of Fame after it was damaged Friday night by protesters.