Zhou rulers claimed that they won the Mandate of Heaven because they

were virtuous and just rulers who were chosen by the gods to govern. They believed that their virtue and righteousness brought them the support and approval of the heavens, allowing them to rule with the divine mandate.

The Zhou rulers believed that their success in battle, their ability to maintain peace and order, and their observance of moral values such as filial piety and respect for ancestors were all signs of their virtuous rule and proof that they had the Mandate of Heaven.

They also claimed that the previous Shang dynasty had lost the Mandate of Heaven due to their corruption and oppressive rule, and that the Zhou dynasty was chosen by the gods to replace them and bring about a more just and harmonious society.

By claiming the Mandate of Heaven, the Zhou rulers sought to legitimize their rule and establish themselves as the rightful rulers of China. They believed that their mandate gave them the divine right to govern and that any challenges to their authority would be seen as challenges to the will of the gods.

In order to maintain their claim to the Mandate of Heaven, the Zhou rulers would often perform rituals and make sacrifices to the gods to show their continued virtue and devotion. These rituals were believed to strengthen their connection with the gods and ensure their continued support.

However, it's important to note that the concept of the Mandate of Heaven was not universally accepted, and different rulers and dynasties throughout Chinese history claimed it for themselves. It was often used as a means to justify and legitimize political power, and rulers would often be overthrown or challenged by rebels who claimed that they had lost the Mandate of Heaven.