Wave propagation in time-independent spatial disorder can be inhibited, a ubiquitous phenomenon known as Anderson localization, arising from the destructive interference of scattered waves. In contrast, dephasing and decoherence, commonly present in out-of-equilibrium systems, are widely recognized to suppress wave interference and thus destroy Anderson localization. Here, we experimentally demonstrate that dephasing can instead induce localization in non-Hermitian quasicrystals, where the eigenstates would otherwise remain delocalized under coherent dynamics. Specifically, the dephasing in our system is realized through uncorrelated spacetime disorder; we thus term the observed phenomenon "spacetime-disorder-induced localization." Our experiments are performed in optical synthetic quasicrystals featuring an incommensurate imaginary potential and a real potential subjected to spacetime disorder. Also, surprisingly, unlike Hermitian quasicrystals where the spacetime disorder obliterates Anderson metal-insulator transition, our non-Hermitian quasicrystals exhibit an exceptionally robust transition against the spacetime disorder. Our experiments challenge the conventional understanding of Anderson localization and open avenues for exploring the unusual interplay between non-Hermiticity, spacetime disorder, and phase transition in quasicrystals.