A recent literature highlights the uncertainty concerning whether economic growth has any causal protective effect on health and survival. But equal rates of growth often deliver unequal rates of poverty reduction and absolute deprivation is more clearly relevant. Using state‐level panel data for India, we contribute the first estimates of the impact of changes in poverty on infant survival. We identify a significant within-state relationship which persists conditional upon state income, indicating the size of survival gains from redistribution in favour of households below the poverty line. The poverty elasticity declines over time after 1981. It is invariant to controlling for income inequality but diminished upon controlling for education, fertility and state health expenditure, and eliminated once we introduce controls for omitted trends.