Deep brain stimulation (DBS) for Parkinson's disease is a highly effective treatment in controlling otherwise debilitating symptoms. Yet the underlying brain mechanisms are currently not well understood. Whole-brain computational modeling was used to disclose the effects of DBS during resting-state functional Magnetic Resonance Imaging in ten patients with Parkinson's disease. Specifically, we explored the local and global impact that DBS has in creating asynchronous, stable or critical oscillatory conditions using a supercritical bifurcation model. We found that DBS shifts global brain dynamics of patients towards a Healthy regime. This effect was more pronounced in very specific brain areas such as the thalamus, globus pallidus and orbitofrontal regions of the right hemisphere (with the left hemisphere not analyzed given artifacts arising from the electrode lead). Global aspects of integration and synchronization were also rebalanced. Empirically, we found higher communicability and coherence brain measures during DBS-ON compared to DBS-OFF. Finally, using our model as a framework, artificial in silico DBS was applied to find potential alternative target areas for stimulation and whole-brain rebalancing. These results offer important insights into the underlying large-scale effects of DBS as well as in finding novel stimulation targets, which may offer a route to more efficacious treatments.