كتب : Mohamed Sabe
Rojas scrambled to connect with a low cross from Salvador Cabanas and watch the ball roll over the goal line dramatically in the 79th minute.
The result means Club America qualify for the CWC semi-finals where they will face European champions Barcelona in Yokohama on Thursday.
Jeonbuk will play Auckland City FC of New Zealand in the 5th place playoff on in Tokyo on Friday.
America wasted a chance to take the lead through Claudio Lopez in the first-half.
The former Argentine international pounced on a miss-pass from Korean keeper Kwoun Sun-tae and looped from 25 meters only to see his effort go just wide.
The Mexicans had goalkeeper Guillermo Ochoa to thank for keeping in the game as he denied two shots from substitute Botti and Brazilian Zecarlo after the break.