So much so, it became a running joke. Chipper Jones and other Braves teammates would smirk or quip every time Redmond reached base. Even Glavine, an eventual 305-game winner, good-naturedly acknowledged the lopsided results.
"We used to joke around," said Redmond, now the Marlins' manager. "I remember sometimes, Chipper and other guys would laugh when they would come to the plate. Even when Tom would come to the plate, he'd say, 'Shocker that you're playing today.' Stuff like that. We'd have a good laugh about it."
The back and forth also occurred later in their careers, after Redmond was with the Twins and Glavine had moved on to the Mets. They met in Interleague Play.
"I was in the American League and he was in the National League," Redmond said. "He'd say, 'Are you getting any hits off anybody else now that you're not in the National League?' I said, 'Oh yeah, I've got a few.' But I respected him so much, I always kept it professional."
The lighthearted in-game exchanges are such a refreshing part of the game. They created memories for Redmond. But in the end, it was Glavine who built a legacy.
On Wednesday, Glavine, Greg Maddux and Frank Thomas were elected to the Hall of Fame.
"It's great to see guys that you played against being recognized for how good they were," Redmond said. "The Hall of Fame is the highest honor in our sport."
Achieving success against an all-time great also is a measure of pride for Redmond. A career .287 batter with a .342 on-base percentage, Redmond boasts a .438 lifetime average and .472 on-base percentage off Glavine.
The results came over a fairly large sample size. Redmond was 21-for-48 with two doubles, two home runs and seven RBIs. He drew three walks and struck out just four times.
"I don't know why I had so much success off him, but I was better off lefties than I was off righties throughout my whole career," Redmond said.
Against lefties, Redmond batted .325, compared to his .266 clip off right-handers.
"As a player, you sit there and you kind of value the guy you're going against," Redmond said. "I knew when I got to the big leagues that Glavine was already one of the best pitchers in the game. Against those guys, you always try to step your game up.
"For whatever reason, I always saw the ball really well. It seemed like it didn't matter what he threw. If he threw me inside or outside, or changeups, I saw the ball so well. It felt like everything I squared up ended up being a hit. I hit a couple of home runs off him, but it was mostly singles."
In the upcoming days or weeks, Redmond hopes to have at least one more exchange with Glavine. This time, by phone. Redmond plans to call Glavine to congratulate him on becoming a Hall of Famer. The Miami manager also is seeking one favor.
"I've always wanted to get a jersey signed by him, just to have in my house," Redmond said. "I think finally now, I can do that. I never felt comfortable asking him for that as a player. Hopefully, there will be a Tom Glavine jersey in my office here in the near future."