Compound drought-heatwave events (CDHEs) have substantially increased since the early 2000s, posing elevated risks to socio-ecosystems. However, the physical characteristics of drought- and heatwave-leading CDHEs and their relative contributions to the overall increase remain unexplored. Using a multihazard pair generation algorithm with daily reanalysis data, we show that this increase is primarily driven by heatwave-leading CDHEs, with the slope of increase in affected land area having risen nearly eightfold, from 1.6 to 13.1% per degree Celsius since the early 2000s. This pattern is evident at the global scale but also shows considerable regional variation. We find that the nonlinear amplification of land-atmosphere coupling since the late 1990s has not only induced the emergence of statistically significant positive sensitivities in previously unresponsive regions, but also markedly enhanced sensitivities in high-occurrence regions. These findings highlight the importance of considering the disproportionate regional risks associated with heatwave-leading CDHEs when adapting to climate change.