Did they? The Guinness Book of World Records will decide in a week.
The current record was set in May by a group of 242 College of William & Mary students who performed the routine in Williamsburg, Virginia, according to Guinness.
Hildago claimed 12,937 people danced Saturday in front of Mexico City's Monument of the Revolution, led by a Michael Jackson impersonator wearing a red-and-gold sequined jacket.
But Guinness must certify whether all those people really performed the entire, intricate routine. The impersonator, who goes by the name Hector Jackson, and most of those in front of a huge crowd of onlookers certainly looked pretty good.
"More people responded than we even imagined!" Hector Jackson said. "Mexico gave the best tribute in the world to Michael Jackson."
Some of those who took part were born more than two decades after "Thriller" was released.
Guillermo Rodriguez, 2, wore a wig of dreadlocks, a black fedora and a white glove as he practiced the moves minutes before the event, holding up a cell phone that blared a recording of the song into his ear.
His father, Guillermo Rodriguez Sr., is not a huge fan himself. But he said his son has become mesmerized by the Jackson videos that Mexican television have often played since the pop icon died June 25.
"Michael Jack!" the toddler screeched, pointing a chubby, un-gloved finger at a Jackson T-shirt held up by a nearby hawker.