Mongols was powerful, but not for long. First, Genghis khan invaded central asia, he was very powerful. Then Batu khan invaded Europe, he was very powerful, mongols defeated many European countries, but mongols was not able to rule them. And mongols never stay in Mascow for a long time. At the last, mongol attacked east Asian countries. at that time, mongols were already weak. The only east asia countries were ruled by mongols are china and korea. So in all places ruled by mongols, Chinese were the lowest class. At that time, mongols lost all wars, which include the wars with Vietnam, java, japan and Burma. so japan defeated mongols, but japan was not powerful.
Storms in 1200s could have helped thwart attacks by Mongolian Emperor Kublai Khan's fleets, a study of lake sediments finds. An ancient story tells of the kamikaze, or "divine wind," that twice saved Japan from Kublai Khan's Mongol fleets. So powerful was the legend that centuries later thousands of World War II pilots known as kamikazes would sign up to protect Japan again, by crashing their planes in suicide missions. Now University of Massachusetts Amherst geologist Jon Woodruff says he has uncovered evidence of some truth to the legend of the ancient kamikazes, typhoon-strength winds that saved Japan from Kublai Khan in the 13th century. http://news.nationalgeographic.com/news/2014/11/141104-kamikaze-kublai-khan-winds-typhoon-japan-invasion/
Japan never defeated the Mongols; while unsuccessful in invading Japan, they were never defeated by the Japanese. Defeat has a different meaning from the way the OP is using the term.
