The power of the Supreme Court of India to decide disputes between the Centre and the States falls under its original jurisdiction as delineated in Article 131 of the Constitution. This provision grants the Supreme Court the authority to hear and decide any dispute involving the Government of India and one or more States, or between two or more States, at the first instance, without the need for an appeal. This original jurisdiction underscores the Court's pivotal role in maintaining the federal balance and resolving conflicts that could potentially impact the governance structure of the country.