As a member of the Ruddlesden-Popper Ln_n+1Ni_nO_3n+1 series rare-earth-nickelates, Pr₄Ni₃O₁₀ consists of infinite quasi-two-dimensional perovskite-like Ni-O based layers. Although a metal-to-metal phase transition at T_pt ≈ 157 K has been revealed by previous studies, a comprehensive study of physical properties associated with this transition has not yet been performed. We have grown single crystals of Pr₄Ni₃O₁₀ at high oxygen pressure, and report on the physical properties around that phase transition, such as heat-capacity, electric-transport, and magnetization. We observe a distinctly anisotropic behavior between in-plane and out-of-plane properties: a metal-to-metal transition at T_pt within the a-b plane, and a metal-to-insulator-like transition along the c axis with decreasing temperature. Moreover, an anisotropic and anomalous negative magnetoresistance is observed at T_pt that we attribute to a slight suppression of the first-order transition with magnetic field. The magnetic susceptibility can be well described by a Curie-Weiss law, with different Curie constants and Pauli-spin susceptibilities between the high-temperature and the low-temperature phases. The single crystal x-ray diffraction measurements show a shape variation of the different NiO₆ octahedra from the high-temperature phase to the low-temperature phase. This subtle change of the environment of the Ni sites is likely responsible for the different physical properties at high and low temperatures.