The majority of the fans wore the singer's trademark black fedora, white gloves and aviator shades for the mass re-enactment of the groundbreaking 1983 video in front of Mexico City's Monument of the Revolution.
Cheers went up as organizers told the crowd that they "beat it," with 12,937 people putting their best foot forward.
The current record was set in May by a group of students in Virginia, according to the Guinness Book of World Records.
Guinness must now certify whether the Mexican fans really performed the entire, intricate dance routine. It was expected to announce its final decision in a week's time.
Saturday's mass dance in Revolution Plaza had its roots in a Facebook group that was joined by thousands of fans.
Organizers held rehearsals for several Sundays leading up to the attempt, and posted a YouTube video for those who wanted to practice but could not attend in person.
The rainy start to the afternoon failed to deter the fans, who withstood the inclement weather to get in a few final practices with their dance steps before the formal attempt.
The downpour let up in time.
"Yes, there's a lot of chaos," said Viridiana Cabrera, who came dressed in full zombie make-up.
"But the truth is that to be in an event like this one on Michael Jackson's birthday is, well, unique," she added.
Jackson impersonator Hector Jackson said the fans gathered in the capital on Saturday had done Mexico proud.
"We raised high the name of Mexico, that was the best," he said.