This paper presents a new efficient solution to the dynamic single source shortest path routing problem, using the principles of generalized pursuit learning. It involves finding the shortest path in a stochastic network, where there are continuous probabilistically based updates in link-costs. The algorithm has been rigorously experimentally evaluated and has been found to be a few orders of magnitude superior to the algorithms available in the literature. It can be used to find the shortest path within the "statistical" average network, which converges irrespective of whether there are new changes in link-costs or not. On the other hand, the existing algorithms would fail to exhibit such a behavior and would recalculate the affected shortest paths after each link-cost update.