The Falcons, 2-1 in preseason play, completed 22-of-32 passes for 223 yards. Harrington hit 13 of 21.
Carson Palmer threw for 136 yards and two touchdowns.
Atlanta led 14-13 at halftime, then scored 10 unanswered points in the third quarter.
Neither team had much of a running game as the Bengals outgained the Falcons in rushing, 86 yards to 74 yards.