Hartley's kick 4:45 into the extra session ended an NFC Championship game that was tied four times and featured a rash of turnovers by the Vikings, including an interception thrown by Brett Favre on a potential game-winning drive in regulation.
New Orleans, which is 15-3 this season, will play Indianapolis in the Super Bowl Feb. 7 at Sun Life Stadium in Miami.
The Colts made it to the big game earlier in the day with a 30-17 victory over the New York Jets.
Drew Brees threw three touchdown passes for the Saints, connecting with Pierre Thomas for 38 yards, Devery Henderson for 9 yards and a 5-yarder to Reggie Bush. Thomas also ran 9 yards for a score.
Brees completed 17-of-31 passes for 197 yards.
Adrian Peterson ran for touchdowns of 19, 1 and 2 yards for the Vikings.
Favre threw a 5-yard touchdown pass to Sidney Rice for the other Minnesota score.
The 40-year-old quarterback finished 28-of-46 passing for 310 yards.
The Vikings lost the ball on three of six fumbles and Favre was picked off twice in a defeat that left them with a season record of 13-5.
Swim Week Miami Beach 2014 [PHOTOS]