Then came the last out: Gary DiSarcina hitting the line drive to center and Greer reaching over his head to grab it for the final out of the historic game.
"Hello, Perfect Game!" Holtz boomed.
Greer was just a rookie in 1994, but that night was just an early indication that he was going to be a special player. That indeed proved to be the case and on a hot Saturday night at the Ballpark, the Rangers showed just how special Greer was by inducting him into their Hall of Fame.
"This is the culmination of 8-10 years of hard work, good teams and good teammates, coaches and managers," Greer said. "As a player you wonder if you did things right. This lets me know that I did something right."
A crowd of around 35,000 let him know that with a standing ovation as he rode into the ballpark on the back of a Lexus convertible. The car took him through the left-field gate down to home plate where several dozen former Rangers were there to honor him, including fellow Hall of Famers Ferguson Jenkins, Jim Sundberg and John Wetteland.
Three messages were read from absent friends. Public address announcer Chuck Morgan read a letter from former Rangers pitcher Darren Oliver, who had been Greer's best friend and roommate when they first came to the big leagues.
Oliver, who now pitches for the Angels, referred to his buddy by his given name, Thurman Clyde, and said, "I can still remember our first Spring Training together when we used to race to the clubhouse in the morning because we were so excited just being in the big leagues. Then we would come home and I would beat you at Nintendo."
Next came a video message from Doug Melvin, who was the Rangers general manager for much of Greer's time in the big leagues, but is now with the Milwaukee Brewers.
"Nobody -- and I mean nobody -- wore the Rangers uniform with more determination and pride than the red-head, Rusty Greer," Melvin said.
Then Morgan read a letter from Gloria Oates, wife of the late Johnny Oates, who managed the Rangers to three division titles in 1996 and 1998-99, but passed away on Christmas Eve 2004.
"Thank you for being such a source of joy to Johnny and me and all who know you," Gloria Oates wrote. "Thank you for your faithfulness and perseverance. Johnny knew he could always count on you!"
The two had a special bond that was really established moments after the final out of the 1995 season. Greer had just finished his second season in the big leagues in 1995 and Oates had finished his first as the Rangers manager.
After the last game, Oates walked by him in the runway to the clubhouse and said, "You're not a platoon player anymore. Next year you're going to be my everyday left fielder."
Greer flourished after that and in a four-year period between 1996-99, he hit .315 while averaging 20 home runs, 105 runs scored and 99 RBIs. He had a .398 on-base percentage and a .502 slugging percentage.
Television broadcaster Tom Grieve performed the induction ceremonies and the crowd roared when he pointed out that Greer had played his entire career with the Rangers and that is unique. No other player in club history ever played nine years in the big leagues and all of them with the Rangers.
That's just one reason why Greer was accorded a 40-second standing ovation when Grieve finished and brought him to the podium for the official unveiling of the plaque.
Greer's speech was short as he thanked his wife Lauri, former coaches and teammates, former managers and general managers and finally the fans.
"You made me feel at home from the first minute I stepped on the ball field here," Greer said. "I was proud and I am proud to have played my 12 years all in a Rangers uniform and in front of you, that's what I'm proudest of.
"Skills diminish, the bat slows, and your legs don't move as fast, you don't throw the ball as fast. But for me, the one thing that won't diminish is the pride that I have in the Texas Rangers organization."
When he was finished, he climbed back into his convertible and made one more tour while the fans gave one more standing ovation to one of the best players to ever play on some of the best ballclubs in Rangers history.