Peru striker Paolo Guerrero twisted superbly to head the winner for the Libertadores Cup holders on the half-hour mark to the delight of the Corinthians fans in Toyota.
"We were expecting a difficult match," Corinthians coach Tite told reporters. "We had huge responsibility on us to win and mentally we were under a lot of pressure."
Corinthians, the first team since 1978 to win South America's premier club competition without losing a game, survived a second-half onslaught from Egypt's Al-Ahly to advance.
Chelsea, whose defence of their Champions League title ended in the group stage last week, face Mexico's Monterrey in the other semi-final in Yokohama on Thursday.
The Chelsea players, stopping to watch the second half of the game in Yokohama's mixed zone after training, will have seen precious little to worry them from the Brazilians.
Ramy Rabia and Elsayed Hamdi missed gilt-edged chances for Al-Ahly, whose players are still scarred by a stadium riot in which more than 70 fans died earlier this year.
Al-Ahly coach Hossam El Badry could hardly mask his disappointment after his side failed to take their chances after dominating the second half.
"I'm frustrated that we lost because it was a really good performance," he told reporters. "We made a mistake and got punished but we deserved to win the game."
European sides have won the last five editions of the Club World Cup, Barcelona lifting the trophy in 2009 and 2011.
Many fans have made the long trip from Brazil to cheer on Corinthians, the first winners of the FIFA competition in 2000.
