BOSTON — Spencer Arrighetti wants the big game.

Since making a rocky big league debut in which he gave up seven runs over three innings to the Royals on April 10, the right-hander has settled in over 21 starts with the Astros. His repertoire has improved, the stuff is better. But Arrighetti’s manager attributed the rookie’s recent success to a shift in mindset and a rise in confidence.

“He’s always been a confident pitcher. But you start seeing more like, ‘I belong, I believe, I want the ball, I want big games,’” Joe Espada said pregame. “When they walk off the mound. When they talk to you. The presence changes. And that’s what’s been the big adjustment for Spencer.”

At a time when Houston has been reeling after a number of injuries to its rotation, the club is reliant more than ever on consistency from the crop of arms that remain. Arrighetti is proving to be just the guy the Astros need.

Following a strong outing in which he recorded a then career-high 12 strikeouts, Arrighetti turned around and set a new career-best with 13 punchouts over seven innings in a 5-4 series-clinching win over the Red Sox on Saturday afternoon at Fenway Park.

Josh Hader closed it out with his franchise-record 25th consecutive save in a season after yielding a leadoff double to Rafael Devers.

“He’s starting to turn the corner and understand how big these games are, and knowing and understanding that every time he takes the mound, it represents an opportunity for us to get closer to our goal. And he’s stepping up,” Espada said. “That performance today? … That’s exactly what this team needs.”

Arrighetti became the first Astros rookie with back-to-back starts of double-digit strikeouts since Tom Griffin had 12 in consecutive starts (June 21 and 25, 1969). The only other Astros rookie to do so is Don Wilson (13 on June 14, 1967, and 15 on June 18). Aside from setting a personal career-high, Arrighetti’s 13 strikeouts are the most by an Astro this season.

Through his first 20 big league starts, Arrighetti struggled most in the first and third innings. Entering Saturday’s outing, 42 of Arrighetti’s 58 earned runs were charged to the right-hander in the first three frames.

On Saturday, Arrighetti retired 12 of the first 13 batters he faced, surrendering his first hit and first charged run of the game on a first-pitch homer to Danny Jansen in the fifth. Arrighetti’s only other earned run came on a home run by Masataka Yoshida in the seventh.

“He’s very effective,” Jansen said. “He’s got four good pitches, maybe five with the changeup. I was trying to get on his heater. I didn’t know it was a cutter until I came into the dugout, honestly.”

Arrighetti worked a five-pitch mix, and continued to show growth in an area that’s challenged him in the past: putting guys away. Entering Saturday, Arrighetti had a .205 batting average against after getting ahead 0-1 in the count, compared to .312 after falling behind, 1-0.

With two outs in the fourth and lefty slugger Rafael Devers at the plate, Arrighetti rebounded from down, 1-0, and got Devers swinging on an 86 mph changeup.

“Just mixing really well,” Arrighetti said. “If you look at it, my four-seam gets hit. That’s one of the reasons I’ve tried to change the pitch mix a little bit in terms of usage percentages. But I think I just did a better job of picking my spots and throwing it somewhere good, and just believing that it’s the right pitch right there.”

With 105 Major League innings under his belt, Arrighetti’s confidence has grown with experience. Some of that is results-based, and a lot is fueled by his teammates.

“I think a lot of it comes from the support system I have here and the support system I have at home as well, just reminders that being me is good, and that’s all I got to do when I’m here,” Arrighetti said.

On Saturday, the Astros offered their support in the form of four homers, including two from Yordan Alvarez. The slugger now has six career homers against the Red Sox, with all of them coming at Fenway Park.

Alex Bregman sent his 16th homer of the season a Statcast-projected 423 feet to center in the seventh inning, before Zach Dezenzo crushed his first career home run — a 437-foot shot to left-center — in the eighth.

After rounding the bases, Dezenzo returned to a silent dugout, with his teammates holding out for approximately 20 seconds before caving and showering the No. 4 prospect with high fives and hugs.