It happened with 10 seconds left in the first quarter on a 9-yard touchdown strike to wide receiver Mike Evans. The Buccaneers had the ball after outside linebacker Shaq Barrett forced a fumble from Bears' rookie quarterback Justin Fields that was recovered by defensive tackle Vita Vea.
Brady was greeted with a giant hug from coach Bruce Arians after the play, while Evans threw the ball to a fan in the stands, not realizing it was a record until Arians told him.
"I said, 'You're gonna have to go give that guy two jerseys to get that ball back,'" Arians joked. "I was like, either get two of Tom's [or two of yours] but you need to get that ball back for him. And he said, 'Does he really want that ball?' And I said, 'I'm betting he wants that ball.'"
A Bucs official was able to retrieve the ball, giving the fan a different one.
"That was really cool. I got it in the bag over there," Brady said. "Mike gave it away. He goes, 'Man, I'm sorry, man. I'll get it.' I said, 'It's alright. I'm sure they'll find a way to get it back.' But I don't actually keep too many things so ... in that circumstance, I just felt like that might be a good one to keep.
"He's gonna get something nice in return. So we'll get him a helmet or a couple jerseys or some other stuff. That was really cool of him to do that."
Brady threw two more touchdowns in Sunday's game, both also to Evans for 2 yards and 8 yards, respectively, in the second quarter. He was replaced by Blaine Gabbert midway through the fourth quarter and finished his day 20-of-36 for 211 yards and four touchdown passes.
Not bad for 44 years of age and just one year after he infamously forgot what down it was against the Bears.
"Every day he comes to practice, he looks like he's 12," Arians said. "The numbers -- they are staggering, they will probably never be broken. I say that, but who knows when the next Tom Brady's gonna come? But they are staggering, but when you watch him practice every single day, you don't see the age."
Sunday also marked the 37th time in Brady's career where he threw at least four touchdown passes and 97th game where he threw at least three, both tying Drew Brees for the most such games in NFL history.
"I just think of all the guys that are sharing it with me," Brady said. "That's the reality. There's nothing about this sport that you do by yourself. It's the ultimate team sport. It challenges you physically, mentally, emotionally, every week, every day at practice -- this is not a sport you can just mail it in.
"It takes 100% of what you have every single day to be successful and I'm just grateful to have amazing teammates, coaches, to be able to do it for as long as I have is a really incredible blessing in my life. I have great family. I've got my little baby girl, who's the biggest cheerleader in the world and her two brothers, who are great cheerleaders and mom who was out there today rooting ... great to have the family here and to win a football game feels really good."
While the milestone was certainly noteworthy and will only add to Brady's glowing list of career accolades, his finest moment of the day was finding a young boy in the stands with a sign that read, "Tom Brady helped me beat brain cancer." Brady placed his cap on the boy's head and shook his hand. The boy began to cry, burying his face in his hands.
"That was really sweet," Brady said. "Obviously a tough kid, man. It puts a lot into perspective of what we're doing on the field. In the end, it doesn't mean much, compared to what people go through. We all try to make a difference in different ways."
The Buccaneers improved to 6-1, the best start in franchise history.