MINNEAPOLIS — There wasn’t much left for Case Keenum to do but fling the ball deep and hope for a miracle.

Miracle answered.

Keenum completed a last-ditch heave near the sideline on the game’s final play Sunday, and Stefon Diggs slithered away for a 61-yard touchdown to give Minnesota a 29-24 victory against the New Orleans Saints and send the Vikings to the NFC championship game.

The Vikings need to win next Sunday at Philadelphia to become a first-time Super Bowl host. The Super Bowl is in Minnesota two weeks later.

Drew Brees had driven the Saints in position for Wil Lutz’s go-ahead 43-yard field goal with 25 seconds remaining, punctuating a steely rally from a 17-point deficit that stood until 1:16 was left in the third quarter.

The Vikings were out of timeouts and nearly out of options when Keenum dropped back with 10 seconds to go from his 39 and threw high into a crowd. Diggs jumped in front of Marcus Williams, who rolled awkwardly underneath Diggs during an ill-fated attempt at a tackle.

Diggs held his ground, kept his feet in bounds and raced untouched into the end zone.

“I’m just thankful,” Diggs said. “They count us out all the time, nobody thinking we can do it. This game was over. I don’t stop playing ’til the clock hits zero. That’s it.”

The Vikings finished 13-3 in the regular season, giving Keenum, a career backup, the keys to the offense when Sam Bradford went down with a knee injury after the opener.

“A heck of a game, wasn’t it?” Minnesota Coach Mike Zimmer said. “And the good guys won.”

Now the Vikings have spun an unprecedented scenario. Next weekend, instead of the usual win-or-go-home stakes, they’re in a win-and-go-home situation.

Though only defensive end Brian Robison remains from the 2009 team that lost in overtime of the NFC championship game at New Orleans, the Vikings exacted some revenge on Brees and the Saints.

Brees connected with Michael Thomas for two of his three touchdown passes in a span of 3:09 of the second half. The first score came after a 12-play, 80-yard drive. The second was set up at the Minnesota 40 by an interception by Williams after an off-balance throw by Keenum, his one costly moment of inexperience or recklessness.

When George Johnson blocked Ryan Quigley’s punt, the Saints took over at the Vikings’ 40. Four plays later, rookie Alvin Kamara, whose breakout was a major factor in the team’s NFC South title and breakthrough from three straight 7-9 finishes, caught a 14-yard pass from Brees for a 21-20 lead with 3:01 left.

Kai Forbath’s 53-yard field goal, his third make of the game against his former team, gave the Vikings their lead back with 1:29 left. That was more than enough time for Brees, the sure-bet Hall of Famer with a Super Bowl ring and all kinds of records.

But after Brees got Lutz in position, there were just enough seconds remaining for Keenum – the undrafted and undersized all-time leading passer in NCAA history at Houston whose first career playoff start ended in spectacular fashion. He finished with 318 yards, going 25 of 40, with Diggs catching 137 yards on six catches.

“This will take a while to get over,” said New Orleans Coach Sean Payton, who fell to 1-5 on the road in playoff games.

Brees saw his 13th career postseason game end in a crushing final moment, his 25-of-40 performance for 294 yards tainted a bit by two interceptions before halftime. One came on a leaping grab by safety Andrew Sendejo, the other off a tip by Everson Griffen that landed in Anthony Barr’s arms at the Minnesota 10 midway through the third quarter.

The Vikings came quickly out of their first-round bye, forcing punts by the Saints on their first three possessions and moving 55 yards in eight plays for a touchdown on their first drive. The shrewd play calling by offensive coordinator Pat Shurmur culminating with a pitch to Jerick McKinnon for a 14-yard run after a fake jet-sweep, showed why he was interviewed by four teams last week for head-coaching vacancies.

Aided by two pass interference calls on Ken Crawley for 54 yards, the Vikings reached the 1 before settling for a short field goal. They pushed the lead to 17-0 early in the second quarter when Latavius Murray plowed in from the 1.

The only other time the Saints went scoreless in the first half of a postseason game was five years ago. They fell behind 16-0 at Seattle in the divisional round and lost 23-15 to the eventual Super Bowl champion.

The first touchdown to Thomas came one play after he leveled Sendejo with a jarring blindside block, sending Sendejo to the sideline for concussion evaluation and reigniting the crowd when the flag that was initially thrown was waved off.