Josh Vaughn ran 65 yards for Atlanta's only offensive touchdown of the game to put the Falcons in front midway through the third quarter.
The Jaguars, however, regained the lead when Kafka drove them 67 yards in 10 plays. Kafka joined the Jacksonville roster during the summer when he was put on waivers by New England. He completed 6-of-15 passes for 65 yards and the lone touchdown.
Dominique Davis saw most of the playing time at quarterback for the Falcons and went 18-of-35 for 17t yards and an interception.
Neither team had won a game coming into their final exhibition contest.
Atlanta will be on the road Sept. 8 to open the regular season against New Orleans. Jacksonville will host Kansas City that day.
2014: The Year in Music [PHOTOS]