The capacity of government agencies to develop effective policy responses to external shocks is an important area of focus for health policy processes, as illustrated by the COVID-19 pandemic. However, few empirical studies exploring sub-national capacity of governments and the influence of institutional, organizational and political factors in shaping the policy response to complex emergencies have been conducted. The purpose of this study is to examine the governance capacity to develop and implement a policy response to a major health emergency—COVID-19—in Tamil Nadu, India, and to understand the factors shaping governance capacity during the first and second waves (2020–2021). Tamil Nadu offers a useful case for exploring governance capacity due to its longstanding public health institutions and previous experiences with disaster and outbreak response. We utilized three sources of data: (1) a review of key policy documents (n = 164); (2) a review of English-language media articles in the Indian press (n = 336); and (3) in-depth interviews with senior decision-makers, technical experts and other stakeholders (n = 10). We present four key findings from this analysis. First, Tamil Nadu’s institutional framework enabled state-level governance capacity during an emergency of massive complexity, allowing for flexibility and nimbleness to adapt to evolving dynamics of centralization and decentralization over the course of the pandemic. Second, the ability to integrate public health expertise was circumscribed at important phases. Third, while coordination with external experts was utilized extensively, engagement with civil society groups was perceived as limited. Fourth, the electoral cycle was perceived by some to have constrained governance capacity at a critical point in the pandemic. By analysing the dynamics of state-level capacity in Tamil Nadu during a complex emergency, this study provides important learnings for other contexts globally regarding the drivers shaping capacity to develop and implement policy responses to crises.