CINCINNATI – Buster Posey insisted all along — even after San Francisco lost the first two at home — that his team was far from done, no matter how long the odds.

Turns out he was right. And the NL batting champion had a lot to do with this most Giant comeback.

Posey hit the third grand slam in Giants postseason history on Thursday, and San Francisco pulled off an unprecedented revival, moving into the championship series with a 6-4 victory over the Cincinnati Reds.

They’ll play either Washington or St. Louis for the NL pennant starting Sunday.

“We could go up against anybody at any time,” shortstop Brandon Crawford said. “Being down 2-0 and coming back and winning three at their place, it’s an unbelievable feeling.”

The Giants became only the eighth team to win a five-game playoff series after falling behind 2-0. Major League Baseball’s changed playoff format this season allowed them to become the first to take a best-of-five by winning the last three on the road.

With one swing, Posey made it possible.

“I don’t think anybody gave up,” he said.

Posey’s second career grand slam off Mat Latos put the Giants up 6-0 in the fifth and sparked a joyous scrum in the San Francisco dugout. The ball smacked off the front of the upper deck in left field, just above Latos’ name on the video board.

“That gave us some breathing room,” reliever Jeremy Affeldt said. “We were all excited.”

Will Clark in the 1989 NLCS and Chuck Hiller in the 1962 World Series hit the other Giants slams in the postseason.

Matt Cain and the bullpen held on, with more help from Posey. The All-Star catcher threw out Jay Bruce at third base to snuff out a sixth-inning rally that cut it to 6-3. The Giants also had a pair of diving catches that preserved the lead in the eighth.

Ryan Ludwick singled home a run in the ninth off Sergio Romo. With two runners aboard, Romo fanned Scott Rolen to end it. The Giants raised their arms, hugged and huddled by the side of the mound, bouncing in unison.

Then they were off to the visiting clubhouse to start spraying some bubbly.

In Cincinnati, the home-field meltdown felt sickeningly familiar. The Reds haven’t won a home playoff game in 17 years.

“You get tired of the disappointments but then you get over it,” Manager Dusty Baker said. “It hurts big-time.”

Once Posey connected, the Reds were the ones facing an unprecedented comeback. They’ve never overcome a six-run deficit in the playoffs, according to STATS LLC.

NATIONALS 2, CARDINALS 1: The Washington Nationals signed Jayson Werth to show them how to win. His game-ending homer extended their surprising season.

Werth led off the bottom of the ninth inning by driving Lance Lynn’s 13th pitch into the left-field stands to give the Nationals a 2-1 victory over the defending World Series champion St. Louis Cardinals and force a deciding Game 5 on Friday in their NL division series.

The homer was Werth’s first with the Nationals but 14th of his career in the postseason. He won the 2008 World Series and a string of division titles with the Philadelphia Phillies before moving to Washington as a free agent before last season on a $126 million contract that stunned much of baseball.

He gets a ton of credit for helping steer a quick turnaround: The Nationals lost 100 games in 2008 and 2009, but led the majors with 98 wins and won their division this year.

Werth’s shot provided a sudden end to a classic postseason contest filled with tremendous pitching. Each team managed only three hits.

Lynn, usually a starter for St. Louis but a reliever in these playoffs, was making his third appearance of this series. He was the wild-card Cardinals’ third pitcher — and faced only one batter.

Drew Storen, who threw the top of the ninth, got the win.