Hartley's kick, from 38 yards, came with 4:42 remaining in the contest.
The victory clinched a first-round playoff bye for New Orleans.
Brees completed 31-of-40 passes for 296 yards and Hartley also kicked a 33-yard field goal.
Chris Redman connected on 13-of-24 passes for 303 yards, including a 50-yard touchdown toss to Michael Jenkins, for the Falcons (6-7)
Jason Snelling scored on a 4-yard run and Matt Bryant kicked 36-, 30- and 27-yard field goals for Atlanta.