[en] Understanding of superconducting phase and vortex states in two-dimensional (2D) superconductors is fundamentally and technologically important. Here we report on low-temperature transport measurements on high-quality ultrathin superconducting Mo₂C crystals containing well-defined line-shaped domain boundaries. We observe pronounced two-stage resistive transition accompanied by an appearance of kink structure well below the superconducting transition temperature, which is related to the development of one dimensional (1D) superconducting phase within the domain boundaries. The resistive transition under the magnetic fields is found to be well described by the thermally assisted collective flux creep model. The magnetic field dependence of activation energy barrier exhibits an enhancement at low fields, indicating a dimensional crossover from 2D to 1D vortex states in Mo₂C crystals. We obtain the entire magnetic field-temperature phase diagram of ultrathin Mo₂C crystals, revealing the existence of additional 1D vortex state induced by the domain boundaries. Our results demonstrate that the domain structures play an important role in determining the superconducting phase and vortex dynamics of 2D superconductors. (letter)