It is the third win in the Dubai World Cup for Bob Baffert, who also trained the legendary Triple Crown winner American Pharoah.
Such is the regard Arrogate is held, Baffert drew comparison after seeing his horse make a remarkable recovery from 20 lengths behind.
"That was 'Plan F'!," said Baffert. "But that's the best I've ever seen in my life, it's unbelievable.
"I guess he knew where he was but it just goes to show you how great this horse is, he's just a great horse. Mike did a great job, he didn't panic."
"He's just amazing. I've never ridden a horse like this," added jockey Smith.
The winning horse's connections, with owner Prince Khalid Abdullah, take home a $6 million prize from the $10 million pot for the Dubai World Cup, making Arrogate the highest earner in racing history.
Florent Geroux, rider of second-placed Gun Runner, believed his horse was in with a chance "until Arrogate arrived, he was just awesome," he said.