Large-scale disasters, such as pandemics and climate-related events, place extraordinary pressure on healthcare providers due to extreme demand surges. Managing these surges is essential to sustaining healthcare resilience. Although numerous studies on healthcare resilience, far less attention has been given to physicians and to how patterns of patient movement can help redistribute demand and alleviate stress on overburdened providers. In this study, we analyzed billions of electronic medical records documenting patient visits to primary care physicians (PCPs) to construct inter-regional patient flow networks across the U.S. During the COVID-19 pandemic, we observed that cross-regional flow rose to 2.81%, compared to the pre-pandemic level of 2.08%. This redistribution absorbed, on average, 58% of the excess stress on PCPs, meaning more than half of the surging demand was handled by patients' moves to less burdened regions, an absolute 43 percentage point improvement from the pre-pandemic baseline of 15%. Further analysis suggests that strengthening cross-regional patient flow could allow the healthcare system to absorb even more stress and reduce the demand for PCPs. These findings provide structural insights for the healthcare system to enhance its pandemic preparedness and disaster responses, and to improve patient care during crises.