<p>A hybrid framework that synergistically combines the extended Kalman filter and small-sample Monte Carlo simulation is achieved for closing moment evolutionary equations of nonlinear stochastic dynamical systems. The novelty of this methodology lies in three aspects: (1) The moment evolutionary equations are constructed and kept in its primary structure-preserving form for both polynomial system and fractional polynomial system. (2) A lower-order moment recursion based on unbiased estimation obtained from a small amount of simulation data and the sampling-induced estimation error capabilities of the extended Kalman filter are leveraged to smartly resolve the issue of moment closure. (3) Validation on polynomial Duffing oscillators and epidemic models with rational incidence rate demonstrates that the proposed method can greatly reduce the root mean square error of lower-order moments with limited additional computational cost. The framework of this paper provides an optimized balance between estimate accuracy and computational efficiency for scenarios where traditional closures fail, thus offering a new paradigm for statistical moment approximation of complex stochastic systems.</p>