In this paper we present a novel construction of non-homogeneous hydrodynamic equations from what we call quasi-Stackel systems, that is non-commutatively integrable systems constructed from appropriate maximally superintegrable Stackel systems. We describe the relations between Poisson algebras generated by quasi-Stackel Hamiltonians and the corresponding Lie algebras of vector fields of non-homogeneous hydrodynamic systems. We also apply Stackel transform to obtain new non-homogeneous equations of considered type.