Context. The estimation of rotation periods of stars is a key challenge in stellar astrophysics. Given the large amount of data available from ground-based and space-based telescopes, there is a growing interest in finding reliable methods to quickly and automatically estimate stellar rotation periods with a high level of accuracy and precision. Aims. This work aims to develop a computationally inexpensive approach, based on machine learning techniques, to accurately predict thousands of stellar rotation periods. Methods. The innovation in our approach is the use of the XGBoost algorithm to predict the rotation periods of Kepler targets by means of regression analysis. Therefore, we focused on building a robust supervised machine learning model to predict surface stellar rotation periods from structured data sets built from the Kepler catalogue of K and M stars. We analysed the set of independent variables extracted from Kepler light curves and investigated the relationships between them and the ground truth. Results. Using the extreme gradient boosting (GB) method, we obtained a minimal set of variables that can be used to build machine learning models for predicting stellar rotation periods. Our models have been validated by predicting the rotation periods of about 2900 stars. The results are compatible with those obtained by classical techniques and comparable to those obtained by other recent machine learning approaches, with the advantage of using fewer predictors. When restricting the analysis to stars with rotation periods of less than 45 d, our models are on average wrong less than 5% of the time. Conclusions. We have developed an innovative approach based on a machine learning method to accurately fit the rotation periods of stars. Based on the results of this study, we conclude that the best models generated by the proposed methodology can compete with the latest state-of-the-art approaches, while offering the advantage of being computationally cheaper, easy to train, and reliant only on small sets of predictors.