The exhibition contest was tied heading into the fourth period, but Josh Scobee kicked a 39-yard field goal that put the Jaguars in front 17-14. His kick ended a 13-play, 75-yard march.
Palmer then drove Jacksonville another 70 yards in nine plays with Richard Murphy finishing off the march on a 5-yard run.
After the teams battled to a 7-7 halftime tie, both sides produced lengthy touchdown passes in the third quarter. Jacksonville's Chad Henne hit Kevin Elliott with a 77-yarder that put the Jaguars in front, but Atlanta tied it on a 49-yard throw from Dominque Davis to Kevin Cone midway through the third.
Henne completed 4-of-6 passes for 106 yards. Davis went the entire game for the Falcons, completing 14-of-24 for 175 yards with a touchdown and two interceptions.
Jacksonville finished the preseason at 3-1 and will open at Minnesota. The Falcons went 1-3 and will get the regular season started in Kansas City.