The Vikings, who have not reached a Super Bowl since their defeat at the end of the 1976 season, have now lost their last five NFC Championship games.
In front of a 71,000 crowd at the Louisiana Superdome, the Saints also thwarted 40-year-old Favre's dream of becoming the oldest quarterback to play in a Super Bowl.
Instead it will be Saints quarterback Drew Brees, who threw three touchdowns, heading to Miami for the showdown with Peyton Manning and the Colts.
Favre, who retired at the end of last season before a change of heart, showed all of his rugged determination and class - although he regretted the late interception.
|Favre recovered from heavy hits drive the Vikings level at 28-28 [GALLO/GETTY]
"I probably should have ran it," he said. "I don't know how far I could have gotten but in hindsight that is probably what I should have done," he said, describing the mistake as "costly".
The Vikings' outstanding running back Adrian Peterson scored three times in a losing cause but a game of this nature was always going to bring injustice along with the rewards and joy.
It was a pulsating encounter with the teams matching each other hit for hit and point for point all the way throughout the four quarters.
The Vikings drew first blood but the teams went in 14-14 at halftime. The next two quarters followed the same pattern with the Saints scoring and the Vikings coming back to level.
Favre, who hobbled after suffering two heavy hits, recovered to help lead the drive which brought the Vikings level at 28-28, Peterson making his third touchdown with a two yard run.
But with 19 seconds left on the clock, Favre, looking to make the ground towards a game-winning field goal, threw a pass toward Sidney Rice which was snaffled up by Tracy Porter to effectively put the game into overtime.
The drama continued as the Saints had to run on a fourth and one to get a first down that allowed them to move into field goal territory, with Pierre Thomas making the crucial yard.
The luck of winning the coin toss for overtime and the steady nerves of Hartley were all that truly separated two excellent teams, although the Saints will feel that having forced five turnovers they deserved victory.
The significance of the win to New Orleans was highlighted by Saints head coach Sean Payton, who recalled when the damaged Superdome was home to thousands of homeless after Katrina.
"This is for everybody in this city. This stadium used to have holes in it, and used to be wet. It's not wet anymore.
"This is for the city of New Orleans," Payton said after receiving the first NFC Championship trophy in the team's 43-year history.
Barely a mile from the downtown venue, fans danced into Bourbon Street, home to the city's Mardi Gras, to begin a long night of festivities.
Brees, who joined the Saints as a free agent half a year after Katrina, described the journey of the team and city as "unbelievable" but also had time to reflect on Favre.
"He's a warrior, he always has been, I remember watching him in middle school. He battled, he is a competitor and he fought to the end, their entire team did. It was a hard fought battle I am just glad we came out on top in the end."
Manning leads Colts
In the AFC championship, the Colts had to come from 17-6 behind to claim their place in the Super Bowl.
Mark Sanchez, the Jet rookie quarterback, had given his side a great start, completing five-of-seven passes for 124 yards and two touchdowns to put the New Yorkers ahead before Peyton Manning struck back.
Manning completed 26 of 39 passes for 377 yards as the Indianpolis avenged a 29-15 loss to the Jets in the penultimate game of the regular season.
"Today wasn't our day," Rex Ryan, the Jets coach, said.
"You have Peyton Manning back there pulling the trigger.
"We tried everything. We tried man. We tried two-man. We tried zone. We tried you name it. You have to give him credit. He's one heck of a quarterback."