Dawson, playing for the Montreal Expos, used that bat to blast three homers -- two in one inning -- and drive in eight runs in a 17-15 slugfest against the Cubs at Wrigley Field on Sept. 24, 1985.
It was one of the most explosive offensive performances of his Hall of Fame career and the reason the bat resides among thousands of artifacts in the sprawling basement vault of the Cooperstown shrine.
The Hawk and his wife, Vanessa, made the customary orientation tour for newly elected members on Tuesday. He'll be inducted along with manager Whitey Herzog and umpire Doug Harvey on July 25.
The Hall of Fame is all about numbers and great achievements, so as Dawson's long day neared an end, I asked him what he was thinking when he picked up that bat and sorted through other memorabilia of his career.
"When I think back, there are so many things that flash through my mind -- how did I ever pull it off, get to this status?" he said quietly, adding "the work that it took, the people you have to surround yourself with, the day-in-and-day-out grind and constant struggles with success and failure. And then to have it all culminated here."
It wasn't about the numbers, the 438 homers, the eight Gold Gloves, a Rookie of the Year Award in 1977 and, 10 years later, the National League MVP Award. Dawson did it the right way.
There were no shortcuts, no hidden agendas to vault him among baseball's greatest.
"I knew I had a special talent, was blessed to be able to stay on track, keep the right mind-set and work ethic to achieve what I did," he said. "When I think back to how I got to this day, that's my mind-set. It wasn't easy. I was driven by discipline that was instilled in me through women who were my mentors: my mother, my grandmother and then my wife -- not people who played the game."
In this era, when steroids and other performance-enhancing drugs have tainted some of the records and achievements, Dawson never wavered from his moral values and respect for the game.
"You control your legacy," he said. "You don't really take the game for granted. My motto in my [acceptance] speech is going to be, 'If you love the game, the game will love you back.'
"That's my message about playing the game the right way. Again, your legacy is who you are, how you carry yourself, your character is what people remember you by. That is something that was important to me. My grandmother always told me your character is who you are as an individual.
"When a player elected to use performance enhancements or whatever, he did it for a reason. Was it the right thing to do? No. That can come back to bite you in the rear end. What's more important? To play the game for fame and fortune? Or play the game to respect it and make sure at the end of the day the fans go home with a smile on their faces whether you win or lose?
"To me, integrity and character is who you are as a player. That's what you'll be remembered by."
When Dawson's former Cubs teammate Ryne Sandberg was elected in 2005, he praised the Hawk during his induction.
"No player in baseball history worked harder, suffered more or did it better than Andre Dawson. He's the best I've ever seen," Sandberg said. "I watched him win an MVP for a last-place team in 1987 [with the Cubs], and it was the most unbelievable thing I've ever seen in baseball. He did it the right way, the natural way, and he did it in the field and on the bases and in every way, and I hope he will stand up here someday."
I guess I never realized how important "doing it the right way" was for Dawson until he virtually shrugged off his specific baseball achievements during the four or five hours I spent with him on Tuesday.
It was almost as if the numbers weren't that important.
What mattered to him the most was that, despite his aching knees -- 14 surgeries and two replacements -- he stuck with it. That made the achievements so meaningful.
It was that dedication that made it possible for him to hit three home runs in that 1985 game, play the outfield so well that he won all those Gold Gloves.
It took him nine years on the Baseball Writers' Association of America ballot to finally get the 75 percent and be called a Hall of Famer.
"I don't think I really felt the true impact of what it is to be a Hall of Famer until I stepped in here today," he said. "It's life-changing. I really got chills. I needed this today. It helps me get my feet under me a little more."
As Dawson walked through the gallery with all the glistening bronze plaques -- his will hang next to Dick Williams, his former Expos manager -- the Hawk looked around and remarked, "I feel like I'm on sacred ground. These are the greatest players who played the game."
And after his long day in Cooperstown, Dawson said said, "I finally feel like I belong."
He didn't say it, but should have added "because I did it the right way."
Hal Bodley is the senior correspondent for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.