BOSTON — Like the rest of his Red Sox teammates, Jackie Bradley Jr. made the most of his second chance.

The bouncer to second base he hit to end the first inning Sunday night stranded the bases loaded. Boston was threatening to blow Game 2 of the American League Championship Series open early, a missed opportunity that looked to be a painful one by the next time Bradley stepped to the plate.

The Red Sox had gone from two-run lead to two-run deficit in the third, and the Astros seemed poised to put a stranglehold on the series. Just three of the 30 teams in either league have fallen short of the World Series after winning the first two games in this postseason round, with Boston the last club to overcome such a deficit in 2004.

Bradley’s three-run double off the Green Monster rescued the Red Sox from facing such long odds this week. That one swing jump-started what was a 7-5 victory at Fenway Park, one that gave renewed hope to the sellout crowd of 37,960 fans on hand.

The series now pivots to Houston for the next three games, and Boston only needs to steal one to ensure another home contest this season. The Red Sox bullpen was strong behind David Price, as four pitchers combined to allow just one run in 4 1/3 frames while protecting what was a 5-4 lead after Bradley’s critical swing. Alex Bregman’s fly to deep left against Craig Kimbrel in the ninth had some Boston hearts fluttering a bit, but an RBI double by Jose Altuve was all Houston had to show for its late rally against the Red Sox closer.

“We’re ready to compete,” Bradley said. “I think everybody is going to enjoy themselves and we’re going to just keep continuing to take it one game at a time.”

Boston did most of its damage in the third, accounting for three of its nine hits to take the lead for keeps. Xander Bogaerts singled up the middle and Steve Pearce ripped a liner to deep left that sent Marwin Gonzalez crashing into the scoreboard. The ball hit the top of his glove and bounced away for a double, putting two men in scoring position, and Rafael Devers drew a four-pitch walk to load the bases.

Bradley dug in one batter later against Astros’ right-hander Gerrit Cole, who held left-handed hitters to just a .519 OPS this season. Bradley sliced an inside fastball down the line in left, with Gonzalez unable to play the carom and all three runners coming around to erase a 4-2 deficit.

“Seems like now he understands who he is as a hitter,” Red Sox manager Alex Cora said. “There’s not too many hard-hit ground balls into the shift. He’s staying through it.”

It was a welcome offensive breakout for a Red Sox lineup that struggled against Houston starter Justin Verlander the previous night. Mookie Betts in particular sparked Boston to life by reaching three times out of the leadoff spot, scoring a run on a passed ball in the seventh and slashing an RBI double to right center in the eighth. Devers also reached three times by singling twice and walking in place of Eduardo Nunez.

“I knew we’ve been really good at turning the page,” Betts said. “And there’s no sense in stopping. We went out and did our thing today.”

Price wasn’t involved in the decision, but the left-hander did leave the game in the fifth with the Red Sox in the lead. Matt Barnes struck out Gonzalez to strand a pair of runners, closing the book on Price after 4 2/3 innings. He allowed a flared two-run double down the line in right by Springer in the second and a bullet two-run homer over the wall in left by Gonzalez in the third, accounting for four earned runs.

“It wasn’t the line I dreamed to have tonight,” Price said. “But our offense, our defense – everybody rallied together. That’s what we’ve done all year.”

Price squandered an early 2-0 lead, as the Boston offense came flying out of the blocks against Cole. Betts cracked a leadoff double off the Bleacher Bar in center and Andrew Benintendi lashed a first-pitch fastball into right center for an RBI single, making it 1-0. Cole put himself in deeper trouble by throwing away a Bogaerts chopper in front of the mound and Devers singled through the left side two batters later double the Red Sox cushion.

“We did a good job attacking him right away,” Cora said. “Mookie hits a double, (Benintendi) hits a single and there were some good swings early in the count.”