Matthew Stafford passed for 217 yards and two late second-quarter touchdowns for the Bulldogs (7-2), who had a tougher game than expected, while winning their third straight.
Georgia has a half-game lead over Tennessee in the SEC East and will play two more conference games at home in the next two weeks against Auburn and Kentucky.
Moreno, who has run for 1,003 yards this season, became the first Georgia freshman with 1,000 yards on the ground since Herschel Walker in 1980.
Omar Haugabook completed 29-of-45 passes for 310 yards and two touchdowns for Troy (6-3), which had won six straight. The Trojans' three losses all came against SEC teams.