On the infinite dimensional space $E$ of continuous paths from $[0,1]$ to $\mathbb R^n$, $n \ge 3$, endowed with the Wiener measure $μ$, we construct a surface measure defined on level sets of the $L^2$-norm of $n$-dimensional processes that are solutions to a class of stochastic gradient system-type equations, and provide an integration by parts formula involving this surface measure. We follow the approach to surface measures in Gaussian spaces proposed via techniques of Malliavin calculus by Airault and Malliavin in 1988.