The Saints fell behind 14-13 early in the final period on Mason Foster's 85-yard interception return for a touchdown for the Buccaneers -- who missed a chance to pad the lead when Rian Lindell missed a 47-yard field goal try in wet, rainy conditions.
Drew Brees took over with just over 1 minute left and began a quick march to the Tampa Bay 9-yard line, with completions to Jimmy Graham, Darren Sproles and Marques Colston, setting up Hartley's game-winning boot.
Brees completed 26-of-46 passes for 322 yards, two interceptions and a TD pass to Graham, who made 10 catches for 179 yards for New Orleans (2-0).
Josh Freeman managed just 125 passing yards on 9-of-22 efficiency with a TD and an interception for Tampa Bay (0-2).
The Bucs' Doug Martin led all rushers with 144 yards on 29 carries.