All these years later, Baker recalls that brief conversation in vivid detail. Some things you just don't forget.
"Right before he went up to hit," Baker said recently, "Hank told me, `I'm getting it over with right now.'
"He'd done that before, where he'd come by and say, `This guy is going to throw me such-and-such pitch, and I'm going to take it over the wall in left-center.' And he'd go do it. So it was nothing new.
"He was pretty amazing that way, but it shows you what kind of hitter he was, how smart he was. Hank wasn't one to talk a lot, you know. But he always knew exactly what he was doing."
The wintry climate, Baker remembers, also played into Aaron's desire to end the chase in his second at-bat that night against Downing, a man known as "Ace" in the Dodgers' clubhouse. Aaron had walked in the second inning, scoring on Baker's double.
"I was trying to hit a home run -- for Hank," Baker recalled.
The young center fielder was shivering as he moved into the on-deck circle in the fourth, Darrell Evans having reached safely on an error in front of Aaron.
"It was freezing," Baker said. "People don't think of Atlanta being like that, but I was in the on-deck circle freezing when he went up to hit. Hank said, `It's cold out here. I'm gonna get this over with right now.' "
As he watched the ball leave Aaron's bat from the on-deck circle, Baker knew the most hallowed record in sports now belonged to his mentor.
Left fielder Bill Buckner made an attempt to climb the fence in pursuit of the souvenir, only to watch Braves reliever Tom House land the prize and run it in to home plate to present it to the man of the moment.
Aaron was mobbed at home plate, but Baker was not among those who rushed to greet him.
"That was Hank's moment," Baker said. "His mom and dad were there, and his kids ran on the field. They stopped the game for a while, and I watched. It was one of those unforgettable scenes."
When the game finally resumed, Baker walked, and after another walk to Davey Johnson, Downing was pulled by Dodgers manager Walter Alston.
The packed house numbering 53,775 was in the process of emptying into the night, Baker recalls, as he faced Downing after the homer and ceremonial delay.
"When I was walking up to hit," Dusty said, "I heard this click-clack all over the park. People were getting up and leaving their seats. They'd seen what they came for, and they were heading home."
Baker, blessed with power and speed and supreme faith in his talents, was 24, California cool, the hippest dude in Atlanta.
Aaron was an old-school Southern gentleman, raised in a whole different world, his waters still but profoundly deep.
And, we've come to discover, he was years ahead of his time.
"Hank understood things," Baker said. "He stressed being a man, accepting responsibility, no excuses. He was like my dad away from home. He made me go to church, eat breakfast, come in from hanging out, dedicate myself to my profession.
"That's a hard sell to a young, single guy. Hank believed in eating right, proper nutrition. He was very regimented in his diet. He was a fish eater, understanding the need to get the right balance of foods."
As a three-time National League Manager of the Year, Baker -- currently an ESPN baseball analyst and thoroughly enjoying Golden State's NBA playoff drive with son Darren -- put Aaron's methods to good use.
"Hank had a huge influence on me in so many ways," Baker said. "That's why I'd bring in good food for my guys -- soul food, good food, the kind of substantial nutrition they needed -- even if it cost me a hundred bucks out of my pocket.
"I didn't want them eating fast food and going out and playing; I think that's one of the reasons we have all these injuries now. Guys are putting low-octane fuel in their systems."
Aaron went to lengths to make sure his young teammates ran on the right fuel.
"I'd have a knock on my door at 8 o'clock when we were on the road," Baker recalled, "and there'd be someone standing there delivering me breakfast.
"I'd say, `What's this? I didn't order anything.' I couldn't figure it out. Then I found out it was Hank. He was putting one of those cards on my door at night and ordering breakfast for me."
When Baker and best buddy Ralph Garr would go to a gym to play some basketball, they'd frequently see Hank there -- but he wasn't working on his jumper. He was sharpening his hand-eye coordination and strengthening his famous wrists and forearms.
"Hank was one of the best handball and racquetball players of all time," Baker said. "You should've seen him. He also played a lot of tennis on a court in his backyard. Everything he did had a purpose.
"That man was always in shape. He played his entire career at 180, 185 [pounds]. He used to work on hand strength. I asked him how he got to be so strong, and he said he worked on an ice truck when he was young."
No media maven, Aaron prefers the background. But that doesn't mean he wasn't at the forefront socially when it was time to stand tall behind the scenes.
"Hank was involved in a lot of things, including the NAACP and civil rights movement -- always in his quiet manner," Baker said. "He knew the prominent people in the movement.
"Hank's not a spotlight grabber, no matter what he's doing. But he's always been actively involved. He deeply cares about people and social conditions."
There's another misconception about Aaron that bothers Baker.
"People have this impression of Hank as being angry," Dusty said. "If he was angry, he'd have good reason. But he's not an angry man.
"He's gotten to the point in his life where he doesn't feel the need to explain himself. Like not coming to see Barry [Bonds] go after his record. People shouldn't read anything into that, about how Hank feels about Barry. He just doesn't want to be in the spotlight. That's Hank's way, staying in the background.
"Besides, at this stage of his life I don't think he cares all that much what people think about him. He's the most secure man I know -- and one of the deepest. There's nobody like Hank."