Television pictures showed the team bus edging its way through the exuberant crowd after arriving at the airport late on Monday amid chaotic scenes.
Photographs showed thousands of Corinthians fans inside the departure hall where they chanted, waved banners and set off fire extinguishers.
The total number of fans was estimated at between 15,000 and 20,000 by local media.
Several hundred fans followed the team bus from the Corinthians training camp, turning the six-km journey into a procession.
South American champions Corinthians go straight into the semi-finals of the Club World Cup, playing their first game on Dec. 12, and are heavily favoured to reach the final where European champions Chelsea, who also have a bye to the last four, are expected to be