During the Heian Period, Japan successfully fought off an invasion by the Mongols of China. What contributed to this success?

The major Mongol attacks on Japan actually occurred during Japan's Kamakura period.

Between 1274 and 1281, The king of the Mongols, Kublai Khan attempted two large invasions of the Japanese Islands.

However, both these invasions resulted in huge losses for the Mongols.

Even though Japan was outnumbered completely and during both invasions Mongols were closed to domination, two 'miraculous' typhoons on both occasions pushed back the Mongols and saved Japan.

Even though invasions took part 7 years apart, the typhoons were able to save Japan and have done down in Japanese folklore as divine intervention.