David Ortiz gazed at his phone, his pursed lips revealing nerves rarely seen from one of the game’s great clutch hitters.

Pedro Martinez’s hand rested on Ortiz’s shoulder, and Martinez grinned when the good news came through. The former teammates embraced, and Martinez welcomed Ortiz into a rare space in baseball history.

Big Papi is bound for Cooperstown — and on the first ballot, too.

Ortiz was elected to the Baseball Hall of Fame in his first try Tuesday, while steroid-tainted stars Barry Bonds and Roger Clemens were denied entry in their final year under consideration by the Baseball Writers’ Association of America.

Ortiz, a 10-time All-Star over 20 seasons mostly with the Boston Red Sox, was named on 77.9% of ballots, clearing the 75% threshold needed for enshrinement. He’s the 58th player inducted in his first time up for consideration.

“Man, it’s a wonderful honor to be able to get in on my first rodeo,” Ortiz said.

Big Papi was among baseball’s most recognizable faces through the 2000s and 2010s. His enormous grin endeared him to fans, but the Dominican’s hulking frame menaced pitchers, especially in the late innings. Three of his 23 career game-ending hits came during Boston’s drought-breaking 2004 postseason, when the Red Sox thwarted the rival Yankees and then won their first World Series title in 86 years.

He’s the fourth Hall of Famer born in the Dominican Republic, joining Juan Marichal, Martinez and Vladimir Guerrero.

“I can imagine how New England has to feel about one of its babies getting into the Hall of Fame today,” Ortiz said. “I’m not even going to tell you about the Dominican Republic.”

The left-handed hitter was signed by Seattle as a teenager and traded to Minnesota as a mi- minor leaguer. He made his major league debut with the Twins in 1997 but hardly looked like a future Hall of Famer there. He was released in 2002, signed by Boston and slugged 31 homers the next season.

Ortiz said he joined the Red Sox to learn what made stars like Martinez, Manny Ramirez and Nomar Garciaparra great. Martinez helped pave the way, encouraging first-year general manager Theo Epstein to sign the 6-foot-3 slugger.

“Once I figured it out, it was going to be a wrap,” Ortiz said. “That team was surrounded by so many superstars, and I went in there like a sponge ready to learn.”

Martinez became a mentor for his countryman. Now, they share the honor of being first-ballot inductees.

“I feel so proud to have been your teammate, to have been your brother, to have been someone there for you when you needed me,” Martinez said. “I’m so glad I have you in my life.

“Well deserved,” he added. “Welcome to Cooperstown.”

Ortiz batted .286 with 541 home runs with Boston and Minnesota while making 88% of his plate appearances as a designated hitter, the most by anyone in the Hall. He passes Edgar Martinez, who was a DH for 71.7% of his plate appearances.