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It’s what amounts to a postseason tradition now, David Price winning a game for the Red Sox and having his 2-year-old son, Xavier, sit on his lap while he conducts interviews afterward.

Eventually the little guy bats the microphone a few too many times and Price hands him off to his wife, Tiffany, as everybody laughs.

In the whirlwind of baseball’s postseason, where reputations can be raised or wrecked in a span of a few innings, Price has finally caught the updraft he has long waited for.

The lefthander pitched well again on Wednesday night, his six strong innings helping lift the Red Sox to a 4-2 victory against the Los Angeles Dodgers and a 2-0 lead in the World Series.

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Related: Photos from the Sox’ Game 2 win

Price and three relievers held the National League champions to three hits. They retired the final 16 batters in a row.

The Sox are the 55th team to win the first two games of the Series. Forty-three of them went on to win the championship. Rick Porcello starts Game 3 in Los Angeles on Friday night and at this point it would be a surprise if the Series returns to Fenway Park.

It’s not that the Dodgers have played badly. It’s more how well and brutally efficient the Sox have been this month. They are 9-2 in the postseason and have won six straight.

David Price game 2 press conference after win over Dodgers

“I’m pumped for myself, pumped for all my teammates and coaches for us to be two wins away,” Price said.

Price couldn’t get through the second inning of his start against the Yankees in the Division Series, another chapter in what had been a career-long struggle in the postseason.

The Sox have since won the three games he started. In the last two, Price has allowed only two runs over 12 innings. He pitched the deciding game of the ALCS at Houston, and on Wednesday he put the Sox in control of the Series.

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Related: Shaughnessy: Suddenly, David Price has morphed into Mr. October

After allowing two runs in the fourth inning, Price set down the last seven Dodgers he faced and wanted to go back out for the seventh inning.

Price relied on his fastball and cutter to control the Dodgers, again showing the ability to vary his mix when needed.

“There’s not going to be questions in spring training about David Price in October,” manager Alex Cora said. “He beat the Houston Astros in Houston. He beat the Dodgers here in Fenway Park. So I’m happy for that because he deserves it. This guy works, he cares about his teammates.”

Alex Cora game 2 press conference after win over Dodgers

All four runs the Sox scored came with two outs. They are 17 of 41 (.415) with two outs and runners in scoring position in the postseason with 11 walks and only eight strikeouts.

“The difference is they got the big hit when they needed and we didn’t,” Dodgers manager Dave Roberts said.

Of the 68 runs the Sox have scored in the postseason, 36 have come with two outs, nine of 12 in the World Series.

Related: Instant Analysis: The Red Sox have been ruthlessly efficient in pivotal moments

October success has become a trend. Going back to 2004, the Sox are 14-2 in the Series, 8-1 at Fenway. After the seven-game heartbreaks of 1946, 1967, 1975, and 1986, the Series has become their playground.

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After winning 108 games in the regular season, the Sox are two wins away from being one of the best teams in the history of their sport.

The every-game-is-vital ethos of the postseason has been a good fit for a team that played a long game all season.

“It’s actually fun because you map out everything over 162 games and you give guys rest and take care of guys, but now it’s like pedal to the metal,” Cora said.

On a 47-degree night at Fenway, the first four Red Sox went down in order against Hyun-Jin Ryu. Xander Bogaerts broke that up with a double to left-center. He then scored on a two-out single by Ian Kinsler.

Related: J.D. Martinez just keeps on hitting, a somewhat silent force for the Red Sox

Down, 2-1, with two outs, nobody on, and the No. 9 hitter up, the Sox scored three runs in the fifth inning to take a 4-2 lead.

Christian Vazquez and Mookie Betts singled before Andrew Benintendi drew an eight-pitch walk to load the bases and force Ryu from the game.

Ryan Madson, who before the game spoke about the difficulty of gripping the ball in cold weather, walked Steve Pearce on four pitches to force in a run.

J. D. Martinez game 2 press conference after win over Dodgers

J.D. Martinez was next. Madson had struck him out on three pitches with the bases loaded in the fifth inning of Game 1.

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“Never a comfortable at-bat for sure,” Madson said. “You know you’re in a pit with a rattlesnake, and one bad move, and you’ll get bit if you’re not paying attention.”

This time, Martinez lined a fastball to right field. With Yasiel Puig playing too deep — he was closer to the retired numbers than the infield — two runs scored as the sellout crowd rattled the rafters at Fenway.

Related: For Andrew Benintendi, an unforgettable catch, a gutsy at-bat, and a new nickname

Martinez has 13 RBIs in 11 postseason games this season and 19 in 18 games for his career.

With Price at 88 pitches, Joe Kelly came on for the seventh inning and retired the side in order. After a rocky second half of the regular season, Kelly has worked 7⅓ innings in six postseason games and allowed one run. Opponents are 4 of 27 (.148) against him.

As he did in Game 1, Cora went to Nathan Eovaldi in the eighth inning. He retired the side in order.

Eovaldi has appeared in five postseason games and allowed three runs over 16⅓ innings.

As a reliever, the righthander has faced 11 batters and retired 10 of them in three appearances.

Craig Kimbrel tore through the Dodgers in the ninth on nine pitches, his command issues now solved.

As caught up as he was in managing the game, Cora noticed how loud and intent the crowd was.

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“They were amazing. They showed up today; they were great,” he said. “I know there’s going to be a few people in Dodger Stadium, that they’re going to be cheering for us, too. We travel well, so it should be fun.”


Peter Abraham can be reached at pabraham@globe.com. Follow him on Twitter @PeteAbe.