Instead of falling on his face, the performance was hailed as extraordinary and one of the year's best. And the critical acclaim was soon followed by box office success by stealing the largest grossing film of 1996, as Captain Steven Hiller in "Independence Day."
"It was one of those moments where I just realized my life was changed forever," Smith recalls.
How did it change?
"You know, it was so bizarre. So bizarre, 'cause the Fresh Prince of Bel-Air is on, and people scream, 'Will! Will! Will!' And on Monday morning, when the box office receipts for 'Independence Day' came out, I was Mr. Smith. 'Good morning, Mr. Smith. Congratulations.' Who the hell's Mr. Smith?" Smith explains, laughing.
A year later, he brought the same sense of style to "Men In Black. It was another huge blockbuster, and as it turned out, all part of Will Smith's plan.
He's been in a lot of movies with special effects and Smith says that's calculated. When he came to Los Angeles to become an actor, he and his manager did some simple research about the movie business.
"And we got the top ten movies of all time, and we realized that ten out of ten were special effects movies," Smith explains. "Nine out of ten were special effects movies with creatures. And eight out of ten were special effects movies with creatures and a love story. So 'Independence Day' and 'Men In Black' were really no-brainers."
There have been a few turkeys along the way, like "Wild Wild West," which was universally panned and still grossed $250 million.
That ability to sell tickets has placed him in the elite company of a handful of actors who can command over $20 million a picture. He lives in a spectacular 200-acre compound outside Los Angeles, far away from the paparazzi, with his wife and two children; daughter Willow and son Jayden have both acted in his films.
His wife is actress Jada Pinkett-Smith, who was a good friend until they became romantically involved.
"When did you two figure out that you two were going to end up together?" Kroft asks Pinkett-Smith.
"Oh, you don't want to know that story. I don't think 60 Minutes is ready for that one," she jokes.
She is every bit his match, in what is widely considered to be one of best marriages in Hollywood. She says when he makes up his mind to do something, it always happens. And he says he to wants to do something big that will change the world for the better.
He has no idea what it s right now, but he has the fame, the money and the platform to do it.
"And you see yourself as a joyful spirit?" Kroft asks.
"Absolutely," Smith says. "I have a great time with my life, and I wanna share it."
Produced By John Hamlin and Albert Kahwaty