We present a novel approach for solving continuous finite-horizon stochastic optimal control problems. To that end, we consider stochastic differential equations from the perspectives of the Wiener chaos expansion and Malliavin calculus. We develop an idea to preserve the feedback character of the occuring Markov control in the stochastic control problem, allowing the reformulation of the original stochastic task as a deterministic one. This facilitates the use of state-of-the-art numerical methods of deterministic optimal control in the context of stochastic differential equations.