NEW ORLEANS -- The odds had to go in Kirk Cousins' favor eventually.

The Minnesota Vikings quarterback, who was 2-10 in his career against teams that made the playoffs and 3-11-1 against teams that entered the game with a winning record, had his chance to flip the script on Sunday at the Mercedes-Benz Superdome.

But Cousins won the first playoff game of his eight-year career, a 26-20 overtime victory over the New Orleans Saints, by way of his own abilities, not through probabilities falling by the wayside.

"He showed the quarterback that we knew he was, the quarterback we knew we were bringing in," Vikings running back Dalvin Cook said. "I’ve been around Kirk for two years now. He’s grown since he got here. That’s part of being in the NFL -- getting better each year, each week that you’re in this game. And Kirk has been doing that. I’m extremely proud of him. We’ve just got to keep going."

Cousins needed to answer the biggest remaining question Minnesota had about him: Could he win in the playoffs and prove his impressive stat lines would add up to wins when it counted most?

The way Cousins performed in his prove-it moment should be all the Vikings need to see to justify signing him to an extension this offseason.

Cousins outdueled Drew Brees, who needed the assistance of Taysom Hill to even stand a chance at a late-game rally. Like he had throughout the season, Cousins benefited from Cook and the Vikings’ running game to move down the field in regulation, which opened up opportunities for play-action throws.

But a nine-play, 75-yard drive in overtime was all about Cousins.

Three key throws -- a third-and-1 pass to Stefon Diggs that went for 10 yards, a 43-yard dime to Adam Thielen that got the Vikings down to the 2-yard line and the 4-yard touchdown pass to Kyle Rudolph -- showed a quarterback poised in the face of pressure. There are plenty who doubted that the same quarterback who threw an interception in the end zone when given the opportunity to be a hero in a Week 2 loss at Green Bay could come through in a gut-check moment.

"To the people that don’t know him, it says what kind of fighter he is, how he prepares, how he goes about his business, and he doesn’t care about the outside noise, per se," Thielen said. "That’s what we see every week. We see it week in, week out, we see the same guy whether it was a miraculous victory or a bad loss. We see the same guy, the way he prepares, the way he treats his teammates and ultimately what kind of person he is."

The Saints are the only 13-win team in NFL history not to make it out of wild-card weekend. In a head-to-head matchup with one of the most explosive offenses in the league, Cousins came away with the type of victory that solidifies the notion that he has indeed reached the "next level" he spoke about so candidly during the offseason.

The challenge now will be doing it again against a San Francisco 49ers team (4:35 p.m. ET Saturday, NBC) with a head coach (Kyle Shanahan) who knows Cousins and how to scheme against his tendencies perhaps better than anyone. The goal is to make Cousins' wild-card performance the new norm.

Cousins can’t rest on the fact that he’s checked off his biggest accomplishment to date. He afforded himself the opportunity to get to do it again on Saturday against San Francisco. Like in New Orleans, it will be up to Cousins to seize the opportunity to add to his postseason record with another standout performance.

"They said he can't win a playoff game, he can't do this," Vikings coach Mike Zimmer said. "He's only been in two, so he's 50 percent -- that's better than a lot of people. I thought he played really well today. He took good care of the ball, he made good decisions. They had some heat on us, and so he had to make some great decisions. It's good. He's gotta go out and prove it again next week, just like we all do."