Which rule states that electrons occupy the lowest available energy orbital?

Aufbau Principle

Explanation:

According to the The Aufbau Principle, the electrons will initialize the filling process of the orbital by filling the available orbitals with the lowest energy first prior to the filling the available orbitals of higher energies.

Since, in order to gain stability, each and every electron in an atom tends to minimize its energy, therefore, the energy of the atom as a whole is also minimum.