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Industry 4.0 brings about a convergence between traditional industrial practices and modern computational techniques. The manufacturing sector is expected to make a greater number of decisions and actions based on the advanced computational analysis of the measurable machinery data. Predictive maintenance of the CNC lathe spindle unit helps the machine avoid unexpected downtimes and meet closer machining tolerances. In this paper, the vibration signals acquired from an experimental run-to-failure test rig are first processed to extract health degradation features, which are then subjected to a neighborhood component analysis-based regression feature selection criteria. Finally, the selected spindle health degradation features are used to train a support-vector machine (SVM) algorithm to evolve a remaining useful life (RUL) estimation model. The SVM hyperparameters that strongly affect the prediction performance are tuned using the Bayesian optimization approach. The evolved predictive model is tested using an independent lathe spindle health degradation data set to obtain the root-mean-square error for predicted and actual RUL. The overall predicted RUL is having an acceptable agreement with the actual RUL. An RMSE equal to 206.23 is obtained as a quantitative measure of prediction accuracy for the Bayesian optimized SVM model for the given dataset. In industrial practice, the evolved SVM predictive model can be employed for the real-time RUL estimation of a similar mechanical system. The proposed predictive model with the integrated feature extraction, selection, and prognosis algorithm can be employed on a real-time spindle health monitoring and predictive maintenance platform for maintenance decision-making. [ABSTRACT FROM AUTHOR]