COVID-19 led to significant and dynamic shifts in power relations within and between governments, teaching us how governments make health policies and how health crises affect government. We focus on centralization and decentralization within and between governments: within government, meaning the extent to which the head of government controls policy; and between governments, meaning the extent to which the central government pre-empts or controls local and regional government. Political science literature suggests that shifting patterns of centralization and decentralization can be explained by leading politicians' efforts to gain credit for popular actions and outcomes and deflect blame for unpopular ones. We test this hypothesis in two ways: by coding the Health Systems Response Monitor's data on government responses, and through case studies of the governance of COVID-19 in Austria, Czechia and France. We find that credit and blame do substantially explain the timing and direction of changes in centralization and decentralization. In the first wave, spring 2020, heads of government centralized and raised their profile in order to gain credit for decisive action, but they subsequently tried to decentralize in order to avoid blame for repeated restrictions on life or surges of infection. These findings should shape advice on governance for pandemic response.