This paper presents a new modification of the least-squares Prony’s method with reduced sampling, which allows for a significant reduction in the number of the analysed signal samples collected per unit time. The specific combination of non-uniform sampling with Prony’s method enables sampling of the analysed signals at virtually any average frequency, regardless of the Nyquist frequency, maintaining high accuracy in parameter estimation of sinusoidal signal components. This property allows using the method in measuring devices, such as for electric power quality testing equipped with low power signal processors, which in turn contributes to reducing complexity of these devices. This paper presents research on a method for selecting a sampling frequency and an analysis window length for the presented method, which provide maximum estimation accuracy for Prony’s model component parameters. This paper presents simulation tests performed in terms of the proposed method application for analysis of harmonics and interharmonics in electric power signals. Furthermore, the paper provides sensitivity analysis of the method, in terms of common interferences occurring in the actual measurement systems.