To overcome the limitations of the sparrow search algorithm and the challenges of dynamic obstacle avoidance in mobile robots, an integrated method combining the enhanced sparrow search algorithm with the dynamic window approach is introduced. First, logistic–tent chaotic mapping is utilized for the initialization of the sparrow population, thereby achieving a uniform distribution of the sparrow population and simultaneously enhancing the exploratory capability of the algorithm. The implementation of the elite reverse learning strategy aims to diversify the sparrow population, thus improving the quality of initial solutions and the algorithm’s search accuracy. Additionally, the position update dynamic self-adaptive adjustment strategy is adopted to enhance the optimization capability of the algorithm by refining the position update formulas for both producers and scroungers. By combining the Lévy flight strategy and the optimal position perturbation strategy, the algorithm’s efficacy in escaping local optima can be improved. Second, an adaptive velocity adjustment strategy is presented for the dynamic window approach and optimized for its evaluation function to enhance the safety of the path. Third, the enhanced sparrow search algorithm is integrated with the dynamic window approach to tackle the problems of the non-smooth global path and inadequate dynamic obstacle avoidance capability. Both simulation and experimental results show the superiority of the enhanced sparrow search algorithm in comparison to other algorithms in terms of the path length, total rotation angle, and algorithm execution time. Notably, in comparison to the basic sparrow search algorithm, there is a decrease in average path lengths by 15.31% and 11.92% in the improved sparrow search algorithm. The integrated algorithm not only crafts local paths rooted in global paths but also adeptly facilitates real-time dynamic obstacle evasion, ensuring the robot’s safe arrival at its destination.