This paper studies the problem of estimation and computation of reliable least-time paths in stochastic time-varying (STV) networks with spatio-temporal dependencies. For a given desired confidence level a, the least-time paths from any origin to a given destination node are to be found over a desired planning horizon. In STV networks, least-time path finding approaches aim to incorporate an element of reliability to help travelers better plan their trips to prepare for the risk of arriving later or traveling for longer than desired. A label-correcting algorithm that incorporates time-dependence of the travel time distributions is proposed. The algorithm incorporates a Monte Carlo sampling approach for a path travel time estimation with time-dependence, which can also be used as an approximate solution method with spatial link travel-time correlations. Numerical results on the large-scale Chicago network are provided to test for the performance of the algorithms and the robustness of solutions. The trade-off between accuracy and efficiency of the approximate solution method compared to a Monte Carlo simulation-based approach is discussed and evaluated.