In recent years, the increasing integration of renewable energy and electric vehicles has exacerbated uncertainties in power systems. Operators are interested in identifying potential violation events such as overvoltage and overload via probabilistic power flow calculations. Evaluating the violation probabilities requires sufficient accuracy in tail regions of the output distributions. However, the conventional Monte Carlo simulation and importance sampling typically require numerous samples to achieve the desired accuracy. The required power flow simulations result in substantial computational burdens. This study addresses this challenge by proposing a surrogate-assisted importance sampling method. Specifically, a high-fidelity radial basis function-based surrogate is constructed to approximate the nonlinear power flow model. Subsequently, the surrogate is embedded in the conventional importance sampling technique to evaluate the rare probabilities with high efficiency and reasonable accuracy. The computational strengths of the proposed method are validated in the IEEE 14-bus, 118-bus, and realistic 736-bus systems through comparisons with several well-developed methods. The comparisons provide a reference for system operators to select the appropriate method for evaluating violations based on the intended applications.