In a lot of cities, Old-Timers’ Day slipped into the same vehicle on the way out of town as the Sunday twinbill. That isn’t the case with the Yankees, who wisely honor their rich tradition.

A big part of the Yankees’ past will be on display Sunday at Yankee Stadium for the 71st Old-Timers’ Day and highlighted by the first member of the Core Four to participate in the ceremony and play in the game.

For certain generations, Jorge Posada and Old-Timers’ Day has a strange ring to it, because other generations remember when Mickey Mantle, Joe DiMaggio, Whitey Ford, Reggie Jackson and Ron Guidry were the headliners.

Yet, Posada is 45 and retired following the 2011 season, so there is a large cluster of Yankees fans whose parents and YES have filled them in about what Posada meant to the Yankees, the only team the switch-hitting catcher played for in a 17-year career.

Ask around about what people remember the most about Posada, and many immediately spit out a two-run double in the bottom of the eighth in Game 7 of the ALCS against the Red Sox and Pedro Martinez that tied the score, 5-5, in a game Aaron Boone won with an 11th-inning homer to send the Yankees to the 2003 World Series.

“I had no chance to catch that, and then nobody was standing on second base. That’s why he was able to get a double,’’ Red Sox center fielder Johnny Damon told The Post this week while vacationing on a lake in Utah. “After that, we couldn’t score any runs.’’

Maybe had the double come off fellow Core Four fraternity member Derek Jeter’s bat it would have been a sizzling line drive into the right-center field gap. But the beauty of watching Posada and Jeter, close friends, was the difference. Jeter was ice, Posada fire. His heart was his face; the powerful arms the arteries. If Jeter made it look easy, every at-bat for Posada seemed to be a grind. Where Jeter glided, Posada plodded.

Yet, when you talk about all-time great Yankees players, Posada is in the conversation. From 2000-07, Posada started an average of 128 games behind the plate, was a five-time All-Star and hit 275 homers. He batted .281 with 30 homers and 101 RBIs in 2003, when he finished third in the AL MVP race.

Posada — who has a plaque in Monument Park, his No. 20 retired and five World Series rings — isn’t going to the Hall of Fame, where Mariano Rivera and Jeter are locks to land. The fourth member of the Core Four, Andy Pettitte, who escorted Mel Stottlemyre to his plaque in Monument Park on Old-Timers’ Day in 2015, has a chance.

That doesn’t diminish what Posada meant to the Yankees, who took the Puerto Rico native in the 43rd round of the 1989 draft out of Calhoun Community College in Decatur, Ala., as a second baseman.

The double against the Red Sox — dropping out of an October night and landing on the grass as Bernie Williams and Hideki Matsui scored as the old Stadium shook — remains crystal clear.

Yet, the moment that defines Posada surfaced in 2000 after the Yankees toppled the Mets in the Subway World Series. The Yankees had lost 15 of 18 and the final seven games of the regular season and finished with a pedestrian 87 wins.

Standing in a champagne and beer soaked visiting clubhouse at Shea Stadium long after the celebration ended, an out-of-town reporter brought up the shaky end to the regular season to Posada.

He looked the reporter in the eye, waved his hands toward the other side of the room and said, “It doesn’t matter, does it? Doesn’t make a difference.’’