A ZnO planar optical microcavity displaying room-temperature polariton lasing has been fabricated. The cavity combines optimum crystalline quality, as given by the ZnO bulk single-crystal substrate employed as active region, and optimum photonic quality, as obtained by the use of two dielectric SiO2/HfO2 Bragg mirrors. A maximum cavity quality factor of about 3000 has been measured, enabling the observation of room-temperature polariton lasing in a wide range of cavity-exciton detuning conditions. Typically, the polariton lasing transition is accompanied by an increase of the output intensity by more than two orders of magnitude, a reduction of the emission linewidth by a factor 5 and a relatively small blueshift of the lower polariton branch (less than 5% of the Rabi splitting).