Electromyogram (EMG) has been a fundamental approach for prosthetic hand control. However it is limited by the functionality of residual muscles and muscle fatigue. Currently, exploring temporal shifts in brain networks and accurately classifying noninvasive electroencephalogram (EEG) for prosthetic hand control remains challenging. In this manuscript, it is hypothesized that the coordinated and synchronized temporal patterns within the brain network, termed as brain synergy, contain valuable information to decode hand movements. 32-channel EEGs were acquired from 10 healthy participants during hand grasp and open. Synergistic spatial distribution pattern and power spectra of brain activity were investigated using independent component analysis of EEG. Out of 32 EEG channels, 15 channels spanning the frontal, central and parietal regions were strategically selected based on the synergy of spatial distribution pattern and power spectrum of independent components. Time-domain and synergistic features were extracted from the selected 15 EEG channels. These features were employed to train a Bayesian optimizer-based support vector machine (SVM). The optimized SVM classifier could achieve an average testing accuracy of 94.39 $ \pm $ .84% using synergistic features. The paired t-test showed that synergistic features yielded significantly higher area under curve values (p < .05) compared to time-domain features in classifying hand movements. The output of the classifier was employed for the control of the prosthetic hand. This synergistic approach for analyzing temporal activities in motor control and control of prosthetic hands have potential contributions to future research. It addresses the limitations of EMG-based approaches and emphasizes the effectiveness of synergy-based control for prostheses.