The cascade hazard, heat stress (preconditioned) and heavy rainfall (response) in close succession have become frequent in several areas of the globe, causing critical infrastructure failures. Although some regions of South Asia witness deadly humid heat stress, little is known about the linkage of humid heat stress (HHS; high temperature compounded by humidity) versus record rainfall and cascade hazard due to compound (same or lagged-day) occurrences of both extremes. We leverage ground-based meteorological records from 1970-2018 to analyze the risk of extreme precipitation preceded by heat stress over selected urban locations of India using a multivariate conditional-probability approach. We show that humid heat is likely to intensify the extreme rainfall, especially during the core monsoon (June-September) season. This phenomenon is associated with moisture convergence and large upper tail distributions of peak precipitation over several sites. Our insights to compound flood hazard would benefit (re)-insurance and flash flood forecast, devising adaptations.