The efficacy of the so-called sensitivity function in developing desensitized optimal control schemes is studied. A sensitivity function provides information about the first order variation of the state under parameter variations at a given time instant along a trajectory. It is demonstrated that the sensitivity function can be employed to effectively desensitize either an optimal trajectory or the state at a particular time instant (for example, the final state) along the optimal trajectory. Zermelo's path optimization problem is chosen to test the theory. Monte-Carlo simulations are carried out, validating the key idea. The limitations of the proposed approach are identified and the possibilities for future work are discussed.