In consideration of the characteristics of two-stage (stable and degraded), nonlinearity and non-stationary randomness in the full life-cycle evolution process of the rolling bearing health indicator (HI), a novel remaining useful life (RUL) prediction method for rolling bearings is proposed based on long short-term memory network–Mahalanobis distance (LSTM-MD) and an incremental unscented Kalman filter (IUKF). First, an LSTM-MD hybrid algorithm is developed to precisely identify the critical change point (CP) between stable operation and incipient degradation in bearing HI trajectories, effectively mitigating the susceptibility of conventional threshold-based methods to HI fluctuations. Second, during the degradation stage, a degradation analysis model based on the nonlinear Wiener process is constructed. Simultaneously, an IUKF-based RUL prediction method for bearings is proposed, which overcomes the implicit assumption of the traditional UKF method that one-step prediction can replace state prediction, particularly in scenarios with significant HI fluctuations, thereby significantly reducing prediction errors. Finally, the proposed method is validated through comparisons with traditional methods using both the XJTU-SY public dataset and a self-built bearing test dataset. The results demonstrate that compared to traditional methods, the accuracy of initial degradation change point identification is improved by 32.6%, and the root mean square error (MSE) of RUL prediction is decreased by 41.8%.