HOUSTON -- With cameras rolling and stage lights beaming upon him, Boston Red Sox pitcher David Price looked down at the precious cargo in his lap as he pondered a question.

"What will you tell him about what this night meant to you?" Price, 33, was asked as he held his toddler, Xavier.

A moment later, Price, still looking at his son, answered: "That it's one of the most special days I've ever had on the baseball field."

In one of the biggest playoff starts of his career, Price effectively put to bed the narrative that he couldn't perform when called upon to open a game when the stakes were the highest.

He did so by getting his first postseason win as a starter in emphatic fashion Thursday, dealing six scoreless innings to help vault the Red Sox into the World Series with a 4-1 win. Boston advances to the Fall Classic for the first time since 2013.

The Red Sox will take on the winner of the National League Championship Series between the Los Angeles Dodgers and Milwaukee Brewers. The World Series begins Tuesday at Fenway Park.

"It's very special for all of us," Price said. "For us to get to [this] point, to do what we did in the regular season, to do what we did against New York in the ALDS and to obviously beat the reigning champs, that was very special for all of us."

Price, who had started 11 playoff games dating to 2011 without earning a victory, struck out a postseason career-high nine batters while walking none.

"That's awesome," Price said of ending his postseason wins drought. "I don't have to prepare myself for [that question] in spring training on Feb. 20, or when September rolls around and I've still got five regular-season starts, I don't have to answer that question anymore."

Price wasn't the only one growing weary of the question. His manager, a former analyst himself, had become frustrated by things he was hearing about his starter in the playoffs.

David Price pitched six scoreless innings in Game 5. Erik Williams/USA TODAY Sports

"I don't want to pick battles with the media," Red Sox manager Alex Cora said, "but I heard somebody [Thursday] on TV just blasting David, blasting him, calling him the worst pitcher in the postseason. Yeah, the numbers are there, I know.

"I don't listen too much to what's going on outside, but that one got me. That one got me. ... But you know what? I'm happy that David showed up. And tomorrow, we can turn the page and move on to the World Series with David Price."

In addition to the nine strikeouts and no walks, Price also limited the Houston Astros, last year's world champions, to three hits.

"Dude, I mean, when you got a pitcher going out there and doing that, it's time to step up," said Red Sox designated hitter J.D. Martinez, wearing an American League champions T-shirt that was soaked in champagne and beer.

"You don't get many performances like that against a offense like that."

To help Price's cause, Martinez slugged a third-inning solo homer off a sign high above the Crawford Boxes in left field in Minute Maid Park. The 396-foot shot put Boston ahead early 1-0.

Three innings later, Rafael Devers' three-run homer gave Price all the cushion he'd need.

"His stuff was amazing, his demeanor on the mound outstanding, he was amazing," Cora said of his starter. "He was great."

It was while Price was walking in from the bullpen following Boston's Game 4 win Wednesday night when Cora signaled to him that he'd be getting this all-important, series-clinching start.

Price had been put in the bullpen in Game 4 as part of an "all hands on deck" situation. Had Andrew Benintendi not made a miraculous diving catch to end that game, Price would have come in, pitching in the ninth after having gotten up twice to warm up.

It was while going through his warm-ups that Price discovered a new trick -- one he wasn't divulging -- that he believed helped his start Thursday.

"I threw 40 pitches in the bullpen [Wednesday]," Price said. "I figured something out warming up in the bullpen, and it kind of just carried over into the game."

Price finished Thursday's outing by retiring seven straight batters, and the Red Sox's bullpen closed out the last three innings for the win.

"I know there was a lot of people thinking he wasn't going to perform, but I knew he was a good matchup for them," Cora said. "Last year he pitched great against the Astros. This year he did the same, too. He was amazing tonight, he was outstanding. I'm very happy for him."

The performance marked a steady improvement from Price's first two playoff starts this season. He lasted less than two innings in Game 2 of the division series against the New York Yankees -- a 6-2 loss -- and gave up four runs in 4⅔ innings in Game 2 of the ALCS, which the Red Sox rallied to win 7-5.

But on Thursday night, Price enjoyed a scoreless postseason start for the first time in his career. Before this outing, the fewest runs he had given up was two in the 2014 ALDS with the Tigers.

"From pitch one, I just had that feeling tonight was going to be that night for him," Red Sox right fielder and ALCS MVP Jackie Bradley Jr. said. "The way he's battled through the whole postseason talk, this and that, it really shows the determination and the competitor that's inside of him to come out here and do it against arguably the top two, three teams in baseball.

"He needed that performance for him. And I don't think he's going to forget it. I'm not."

Price induced a playoff career-high 15 swing-and-misses, according to TruMedia. He mostly relied on his changeup, throwing it 42 percent of the time, a high for Price in any start, including the regular season. Astros hitters went 0-for-10 in at-bats that ended in a changeup, including five strikeouts.

Asked -- in between multiple interview interruptions because of champagne and beer showers from his teammates -- about what made his changeup so effective, Price offered a simple explanation.

"They weren't hitting it," he said.

He later expanded upon that thought while sitting at the podium.

"It was good in the bullpen warming up, and it got better as the game went on," Price said. "Made some adjustments with it after the fourth inning, and it was huge."

Following his sixth-inning strikeout of Astros DH Jose Altuve, Price let out some emotion as he walked off the mound. He had just faced his final batter of the game and knew it. Two batters earlier, Price was shouting his appreciation into right field as outfielder Mookie Betts kicked off the inning with a leap near the wall to come down with a spectacular catch.

"I was happy, man. Just going through 1-2-3 in that part of that lineup ... that was huge," Price said.

Price's nine strikeouts were the most by a Red Sox pitcher in a potential clinching game, breaking the previous record of eight shared by Roger Clemens, Pedro Martinez (twice) and Jon Lester.

Price pitched in relief in the 2008 World Series as a rookie with the Tampa Bay Rays, but he has never started on the game's biggest stage. After his effort in Houston, he's about to get his chance.

When he makes this trip to the World Series, his first since that rookie year, Price promises to fully soak in the moment.

"I remember the first time I ever went, I'm out there shagging in left field before Game 1, and [Phillies pitcher] Jamie Moyer pulls me aside," Price said. "He had [22] years in the big leagues, and that was the first time he ever got to that point. So he told me to make sure that I enjoyed it and to really appreciate how special it was to get to that point at the time.

"I definitely didn't. I got called up Sept. [14], and had two weeks in the big leagues before the playoffs. I hadn't gone through the grind yet. I hadn't experienced my failures at the big league level like I have now. So to get back to that point is pretty special."

The pennant was a perfect 43rd birthday present for rookie manager Cora, who became the first skipper from Puerto Rico to take a team to the World Series.

"I'll take it," Cora said.

Bradley, who hit big home runs in Games 3 and 4, finished with nine RBIs in the series to earn his ALCS MVP award.

"It kind of just all boils down to having a game plan and obviously executing," Bradley said. "You can have a game plan, but sometimes it might not work out. But as a batter, you want to swing at good pitches. You want to swing at pitches you can handle."