Photovoltaic energy is a key contributor to the global transition toward renewable and sustainable electricity generation using solar panels. This study explores the use of Halley’s Method for Multivariate Optimization (a third-order technique) to precisely estimate the intrinsic electrical parameters of single-diode solar cells. By tackling the nonlinear nature of the solar cell equations, the method seeks to reduce the discrepancy between measured and simulated current values. In contrast to Newton’s approach, which provides quadratic convergence, Halley’s method produces cubic convergence. This indicates that with well selected beginning circumstances, it may discover the best solution in less iterations. In low-dimensional situations when the computation of higher-order derivatives is still inexpensive, it ensures faster and more stable convergence, this technique required 12 iterations to converge for a single solar cell and took 0.12 s. In this study, an RTC France solar cell is used, and experimental current-voltage measurements are applied to define the objective function. The electrical parameters estimated using Halley’s method are then evaluated against results obtained from recent optimization strategies, including metaheuristic, iterative, and analytical methods. To assess performance, statistical indicators such as Individual Absolute Error (IAE), Relative Error (RE), and Root Mean Square Error (RMSE) are employed. The proposed approach demonstrates high precision, achieving an RMSE as low as 0.001067, indicating a strong alignment between simulated and experimental data. Additionally, the MCO-R method shows promising results, with an RMSE of 0.0015, followed by SCA (0.0072) and LW (0.00969). Moreover, the R2 of this approach is 99.9%, and the MAE is 8.10 × 10−4.