NEW YORK -- There seemed to be little anxiety as Deivi García deconstructed the Mets' lineup on Sunday, displaying remarkable poise throughout his Major League debut. He shrugged as though it should be obvious: no matter which mound he has set foot upon throughout his 21 years, he has always envisioned pitching at Yankee Stadium.

Rated as the Yankees' No. 3 prospect by MLB Pipeline, García offered a glimpse of the future and Gary Sánchez made history by slugging the first extra-inning pinch-hit grand slam in franchise history, powering a 5-2 victory to complete a sweep of a Subway Series seven-inning doubleheader in the Bronx.

• Box score

"I wasn't nervous," García said through a interpreter. "I definitely understood the task in front of me, and I wanted to do the best I could to help my teammates."

Selected as the 29th man for Sunday's twin bill, García became the first pitcher in Yankees history to debut with least six or more innings with no earned runs and no walks. He showcased a sneaky fastball and a terrific curveball, scattering four hits across a 75-pitch performance.

"Nothing really seems to faze him," manager Aaron Boone said. "He was having fun tonight the whole time. You'd see him walk in after an inning like it was no big deal. He'd kind of smile and make some jokes. It was fun to watch him compete."

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The Mets scored an unearned run facing García in the sixth, as Luke Voit muffed a Jeff McNeil grounder and Dominic Smith lined a run-scoring hit into left field. García finished his outing in strong fashion, inducing a double play that ended the sixth inning, earning praise from his teammates as well as a prominent fellow Dominican.

"Deivi Garcia's presence on the mound was outstanding, and his balance on the mound too!" Hall of Famer Pedro Martinez said on Twitter. "I was impressed with the way he commanded his pitches today."

The decision to have García start the second game of the doubleheader revolved around maximizing the rookie's comfort level, according to Boone. Summoned from the alternate training site in Moosic, Pa., García stayed in a New York hotel Saturday night and the Yankees wanted to allow him time to huddle with Erik Kratz for game planning purposes.

Kratz has forged a strong bond with García, having teamed last season at Triple-A Scranton/Wilkes-Barre and at the alternate training site this year. García calls Kratz "padre," or father, and as Kratz jogged out for García's warmups, the veteran shouted to the Yankees' dugout: "I'm so excited to play catch with my son!"

With the 40-year-old Kratz behind the plate, the age gap was the largest of any Yankees battery since Aug. 30, 1906, when the franchise was still called the Highlanders and 21-year-old Cy Barger pitched to 42-year-old Deacon McGuire.

"I thought he and Kratzy were on a good page together," Boone said. "It was fun to watch him go through a really good lineup there and have the weapons to do it."

After the sixth inning, García found Kratz on the bench, relaying Boone's message that their work was complete for the evening. Kratz embraced García, congratulating him on a job well done.

"He's a man with a lot of knowledge," García said. "I try to listen and pay attention and follow his guidance."

With Tyler Wade's third-inning homer off Seth Lugo standing as the Yankees' only offense until Sánchez came off the bench to slug his grand slam, García had to settle for a no-decision, though he didn't seem to mind.

Asked what memory he would savor from his debut, García said that he'd treasure his first strikeout, freezing Smith with an 84.5 mph changeup that ended the first inning. Though García returned to the alternate training site after Sunday's game, he can be confident that there will be more big league opportunities to come.

"I think it's an advantage to keep your emotions in check and not show any weakness at all," Garcia said. "You're battling out there, and when you do that, you keep that calmness. You focus on your job."