Smith (25-5) put on a display of counterpunching manager Floyd Mayweather Jr would be proud of as he won his first world title at the age of 34.
Smith, who becomes the first Las Vegas-born boxer to win a world strap, was emotional following the announcement.
"It means everything," the fighter, who contemplated suicide after the failure of his marriage, said. “I didn't think I'd be here.
"Man, I've waited 13 years for this... It's amazing because five years ago I was about to kill myself and I didn't do it. And now I'm here, 13 years later, a champion."
He said he was cut in training for the bout and also suffered a rib injury.
"Floyd asked if I wanted to pull out and I said I didn't want to pull out," Smith said. "This was the biggest moment of my life."
Mayweather, who wrote to Smith while in prison last year, said: "I've been boxing Ishe since we were both younger. I'm so proud of him. When everybody turned their back on him, I didn't want to do that. I told him that not only could he fight for Mayweather Promotions, but I was going to get him a title shot."
Bundrage (32-5) tired in the later rounds and was cut in the ninth after being caught by Smith, who did not risk his obvious lead as he secured victory on the cards 116-111, 116-111, 113-114.
"Ishe just fought a good fight. He won the fight fair and square," Bundrage said. "I didn't follow instructions. He won it. Congratulations to him."
Detroit fighter Bundrage, 39, had defended the belt twice -against Cory Spinks, the man he won it from in 2010, and Sechew Powell.