The economic impact associated with power quality (PQ) problems in electrical systems is increasing, so PQ improvement research becomes a key task. In this paper, a Stockwell transform (ST)-based hybrid machine learning approach was used for the recognition and classification of power quality disturbances (PQDs). The ST of the PQDs was used to extract significant waveform features which constitute the input vectors for different machine learning approaches, including the K-nearest neighbors’ algorithm (K-NN), decision tree (DT), and support vector machine (SVM) used for classifying the PQDs. The procedure was optimized by using the genetic algorithm (GA) and the competitive swarm optimization algorithm (CSO). To test the proposed methodology, synthetic PQD waveforms were generated. Typical single disturbances for the voltage signal, as well as complex disturbances resulting from possible combinations of them, were considered. Furthermore, different levels of white Gaussian noise were added to the PQD waveforms while maintaining the desired accuracy level of the proposed classification methods. Finally, all the hybrid classification proposals were evaluated and the best one was compared with some others present in the literature. The proposed ST-based CSO-SVM method provides good results in terms of classification accuracy and noise immunity.