BOSTON -- Five days before this American League Division Series started, amid the euphoria of a sudsy celebration that marked the clinching of the AL East, Boston Red Sox owner John Henry contemplated the postseason impact David Price could make as a relief pitcher.

Actually, Henry already had witnessed it firsthand.

"It was 2008 when he came in and shut us down from the bullpen," Henry said, referring to Price's role in helping the Tampa Bay Rays vanquish the Red Sox in a seven-game AL Championship Series played almost a decade ago. "Maybe we'll see that again this year. I think we will."

Not an unreasonable request from the man who paid Price $30 million this year. Sure enough, when the Red Sox needed him most Sunday in Game 3 against the Houston Astros, darned if Price didn't turn in the best relief appearance the franchise had seen since Pedro Martinez shrugged off a bad back to throw six scoreless innings in Game 5 of the division series in 1999.

This game, like that one, had win-or-go-home implications. This game, like that one, saw the Red Sox fall behind early by three runs but rally to take a lead. This game, like that one, required a former Cy Young Award winner who had been compromised by injury to rise up and shut down the most powerful lineup in the league.

The final score -- 10-3 Red Sox, who extended their season by at least one more day -- betrays how tense it was during the four innings Price stood on the mound. When he entered in the fourth inning, the Red Sox had their first lead of the series, 4-3, on baby-faced rookie Rafael Devers' two-run homer. When Price left to a thunderous ovation after the top of the seventh, it was still 4-3, with the Astros' mighty offense stuck in neutral.

"The story of this one is David Price," Red Sox manager John Farrell said. "Clearly."

Indeed, there were other Game 3 heroes. Devers hit the team's first home run of the series, in the 21st inning of the it, to bring the Red Sox all the way back after starter Doug Fister left them in a 3-0 first-inning hole. Mookie Betts reached over the short, right-field fence to rob Josh Reddick of a three-run homer in the second inning and saved at least four runs overall. And Hanley Ramirez became the third player in Red Sox history to go 4-for-4 in a playoff game after holding a "Believe In Boston" banner aloft as he ran onto the field for pregame player introductions.

But it was Price, of all people, who saved the season.

"It feels good to put up zeroes in the playoffs," Price said. "That's why I signed here."

But Price has been criticized, even derided, during his brief tenure in Boston. He didn't help himself with a much-publicized June 30 humiliation of Hall of Fame pitcher/team broadcaster Dennis Eckersley on the team plane. And then there's his performance in the playoffs. He's 0-8 with a 5.74 ERA in nine career postseason starts, including a dud in Game 2 of last year's division series against the Cleveland Indians.

Price would be starting this October, too, if not for a seven-week stint on the disabled list with left-elbow inflammation. There wasn't enough time before the playoffs for him to build back the arm strength to throw six or seven innings, so the Red Sox put him in the bullpen with the hope that he could be their version of Indians relief ace Andrew Miller.

Through five late-season relief outings and an appearance in Game 2 against the Astros, Price didn't disappoint, tossing a total of 11 1/3 scoreless innings and holding opponents to a .103 average. But he didn't throw more than 40 pitches or 2 2/3 innings in any of those games.

"We talked about how much he could give us before [Sunday's] game, and he mentioned, 'I've got 80 pitches,'" Farrell said. "Little bit of a surprise."

Said Price: "I don't know. I just told him that, to be honest. Just felt all right."

Farrell took Price at his word. Summoned into a one-run game, Price worked around a one-out single to Yuli Gurriel in the fourth inning, then escaped a two-on, none-out jam against the heart of the Astros' order in the fifth before cruising through a 10-pitch sixth.

And when Price said he was OK to continue, Farrell sent him back out for the seventh. After issuing a one-out walk to AL MVP front-runner Jose Altuve, he got cleanup hitter Carlos Correa to line out to Betts and struck out Marwin Gonzalez on an elevated fastball.

The proud owner of a dog named Astro, Price likes to call himself "Astro's Dad." On Sunday, he was the Astros' daddy.

"He's letting it fly," Red Sox assistant pitching coach Brian Bannister said of Price. "He's pitching with that almost-closer mentality, but he's doing it for an extended period. Most guys wear down. What's impressive is he just keeps coming in and saying, 'I want to pitch another one.' It says a lot because he's digging his heels in for the team."

But Price believes he has even more to give.

In all likelihood, Price won't be able to pitch Monday in Game 4, but the game could be pushed back a day with rain in the forecast. The Red Sox haven't discussed his role in a potential Game 5, but it almost certainly would be out of the bullpen.

Now, though, after being stretched out to nearly 60 pitches, Price was asked if he believes he could start a game if the Red Sox somehow win two more against the Astros and move on to the ALCS.

"I would love to," he said before continuing. “I can do this as a starter, too. I just haven’t done it yet. Period. If I throw well out of the bullpen, that doesn’t mean anything. I’ve got to do this as a starter. I know that, y’all know that, y’all write it and it will be talked about.”

Has he discussed the possibility with Farrell?

"No, we have not."

The Red Sox have too much to do before that becomes an option. But if not for Price, they wouldn't even have the opportunity to consider it.