Using a single N-body simulation we explore the formation, evolution, and spatial variation of the phase-space spirals similar to those recently discovered in the Milky Way disk. For the first time in the literature we use a self-consistent N-body simulation of an isolated Milky Way-type galaxy to show that the phase-space spirals develop naturally from vertical waves driven by the buckling of the stellar bar. Such vertical oscillations trigger the formation of various time-dependent phase-space spirals in the entire disk. The underlying physical mechanism implies the link between in-plane and vertical motion that leads directly to phase-space structures whose amplitude and shape are in remarkable agreement with those of the phase-space spirals observed in the Milky Way disk. In our isolated galaxy simulation, phase-space spirals are still distinguishable at the solar neighborhood 3 Gyr after the buckling phase. The long-lived character of the phase-space spirals generated by the bar buckling instability cast doubts on the timing argument used so far to get back to the time of the onset of the perturbation.