Tropical rainforests have experienced episodes of severe heat and drought in recent decades, and climate models project a warmer and potentially drier tropical climate over this century. However, likely responses of tropical rainforests are poorly understood due to a lack of frequent long-term measurements of forest structure and dynamics. We analyzed a 12-year record (1999–2010) of 47 817 annual measurements of canopy height to characterize the response of an old-growth Neotropical rainforest to the severe heat and drought associated with the 1997–1998 El Niño. Well-drained soils on slopes and plateaus experienced a threefold increase in the fraction of the landscape in gaps (≤2 m) and a reduction in the fraction in high canopy (>15 m) causing distributions of canopy height to depart from equilibrium for a period of 2–3 years. In contrast, forests on low-lying alluvial terraces remained in equilibrium and were nearly half as likely to experience upper canopy (>15 m) disturbance over the 12 years of observation. Variation in forest response across topographic positions suggests that tropical rainforests are more sensitive to moisture deficits than high temperature and that topography likely structures landscape-level variation in the severity of drought impacts.