Unbeaten Crawford had knocked down Spence three times and had his previously unbeaten foe staggering under a hail of blows when referee Harvey Dock called a halt at 2:32 in the ninth.
Crawford added Spence's World Boxing Association, World Boxing Council and International Boxing Federation titles to his own World Boxing Organization crown.
Crawford became the first undisputed welterweight world champion of boxing's four-belt era, which began in 2004.
A former lightweight and undisputed light welterweight world champion, he became the first man to win all the belts in two weight divisions.
"It means everything because of who I took the belts from," Crawford said.
"They tried to blackball me, they kept me out, they kept me out. They talked bad about me, they said I wasn't good enough, that I couldn't beat these top welterweights, and I just kept my head to the sky and I kept praying to God that I would get the opportunity to show the world who Terence Crawford is."
"And tonight, I believe I showed how great I am," added Crawford, who improved to 40-0 with 31 knockouts, taking his string of knockouts to 11 fights.
That includes all eight of his fights at welterweight.
It was a stunningly dominant performance in what was expected to be a close fight, one that had drawn comparisons to classic welterweight match-ups such as Roberto Duran v Sugar Ray Leonard and to more recent mega-fights like Floyd Mayweather's 2015 victory over Manny Pacquiao.
Music superstar Eminem provided in-person accompaniment for Crawford's walk to the ring. The sellout crowd at T-Mobile Arena included a who's-who of boxing royalty headlined by heavyweight greats Mike Tyson and Evander Holyfield and also featuring Mayweather and Pacquiao.
Spence made the running in the opening round, but Crawford, fighting southpaw, began to let his hands go in the second, punishing Spence with a piston-like jab that dropped him at the end of the round.
Flash knockdown
"That was more of a flash knockdown," Crawford said. "I caught him with a left and he didn't think I was coming back with the right."
Spence was still moving forward in round three, but the power and accuracy of Crawford's counter punches were devastating.
Crawford landed a series of hard punches in the fourth, including a left that rattled Spence.
It was more of the same in the sixth, and in the seventh Crawford had Spence down again with a right uppercut followed by a hook to the ear.
He dropped him again with a blow to the chin in the waning seconds of the round.
Spence, who had never before been knocked down, fell to 28-1 with 22 knockouts.
He came out for the ninth still looking for the big punch that might turn things around. But Crawford was landing at will with Spence struggling to stay on his feet when the referee brought it to a close, sparking a celebration for Crawford who then had an embrace and words of encouragement for his beaten rival.
Spence was fighting for the first time since a 10th-round stoppage of Yordenis Ugas in April of last year.
He didn't fight in 2021, when a planned bout with Pacquiao was scuppered by a torn retina that required surgery.
But he said ring rust wasn't the problem.
"He was just better tonight," said Spence, who was already agitating for a rematch that he said he hoped would be at the higher weight limit of 154 pounds.
