The Song (also known as "Sung") Dynasty, (960-1276) achieved dominance because of advancements in technological innovations that eluded other cultures. The Song Dynasty improved efficiency and yield in agriculture. They refined and improved iron working, forging better weapons and structures. They also improved printing, enabling more information to be disseminated to the literate.
The Song form of governance also helped them achieve dominance. Their high posts were filled with scholars who had to pass very competitive written examinations.
It is a mistake, however, to assume that the Song Dynasty was completely dominant. While they certainly were able to surpass others in these areas, military dominance was not something they pursued. Instead, they focused on maintaining peace with their neighbors.