We established a continuous-time framework for entangled quantum Markov chains derived from classical continuous-time Markov processes. Unlike previous studies focused on discrete-time dynamics, we demonstrated that a robust mixing property emerges directly from the structural architecture of the underlying continuous-time process. Our analysis showed that inhomogeneous entangled chains exhibited path-independent convergence to a limiting distribution determined by asymptotic temporal parameters. The results motivated future study of these entangled Markov chains in connection with open quantum system dynamics and quantum master equations.