Accurately detecting symbols transmitted over multiple-input multiple-output (MIMO) wireless channels is crucial in realizing the benefits of MIMO techniques. However, optimal MIMO detection is associated with a complexity that grows exponentially with the MIMO dimensions and quickly becomes impractical. Recently, stochastic sampling-based Bayesian inference techniques, such as Markov chain Monte Carlo (MCMC), have been combined with the gradient descent (GD) method to provide a promising framework for MIMO detection. In this work, we propose to efficiently approach optimal detection by exploring the discrete search space via MCMC random walk accelerated by Nesterov's gradient method. Nesterov's GD guides MCMC to make efficient searches without the computationally expensive matrix inversion and line search. Our proposed method operates using multiple GDs per random walk, achieving sufficient descent towards important regions of the search space before adding random perturbations, guaranteeing high sampling efficiency. To provide augmented exploration, extra samples are derived through the trajectory of Nesterov's GD by simple operations, effectively supplementing the sample list for statistical inference and boosting the overall MIMO detection performance. Furthermore, we design an early stopping tactic to terminate unnecessary further searches, remarkably reducing the complexity. Simulation results and complexity analysis reveal that the proposed method achieves exceptional performance in both uncoded and coded MIMO systems, adapts to realistic channel models, and scales well to large MIMO dimensions.