CLEVELAND — Though CC Sabathia didn’t make the All-Star Game in his final season, he nabbed a pretty solid consolation prize.

The Yankees’ big lefty, who started his career here with the Indians, revealed on Monday that he will be throwing the ceremonial first pitch for Tuesday’s Midsummer Classic. American League manager Alex Cora of the Red Sox and Major League Baseball invited him to participate as a token of appreciation for his contributions to the game.

“It wasn’t difficult to say yes to it,” Sabathia said at the Huntington Convention Center of Cleveland. “I think if you had asked me at the beginning of the year about coming to the All-Star Game, I probably would’ve been like, ‘Nah.’ But as I’ve gotten into this throughout this year and everything, coming here the first time [the Yankees visited the Indians last month] and seeing the All-Star Game was here, I thought it would be cool to come back.

“I was trying to make the team. Obviously, I ain’t got that kind of skill anymore. But to have Alex [Cora] want to bring me here and MLB go along with it, it’s just amazing. It feels good.”

Cora called him about two months ago, Sabathia said. Having last made the All-Star team in 2012, he said he was especially excited to bring his daughters Jaden, 13, and Cyia, 10, for their first All-Star Game.

Sabathia owns a 4.03 ERA for the Yankees in 14 starts totaling 76 innings.

If Tuesday’s game is tied after nine innings, MLB will enact its new, collectively bargained rule calling for each team to begin its half inning with a runner on second base.

“I’ve seen the rule play before, internationally. And it’s kind of like the coolest, [toughest] thing ever in baseball, to be honest with you,” Cora said. “With one pitch, it changes the game. It is what it is.”

As for whether baseball should consider deploying the system for regular-season games in the hopes of avoiding marathon contests, “I like the way the game is played now,” Cora said. “And hopefully it stays that way.”

Added National League manager Dave Roberts: “Probably the wrong thing to say, but I kind of like it the way it is right now.”

Cora said Yankees starting pitcher Masahiro Tanaka will relieve starting AL pitcher Justin Verlander, most likely in the second inning, and that if the AL owned a lead in the ninth inning, Yankees closer Aroldis Chapman would be tabbed for the save. The Dodgers’ Hyun-Jin Ryu will start for the NL, and Roberts said he would follow Ryu with Dodgers legend Clayton Kershaw and reigning NL Cy Young Award winner Jacob deGrom of the Mets.